Homework 1 Parts Of A Circle Area And Circumference Answers? Top 50 Best Answers

This site is a one stop shop for all your exercises in finding the area and perimeter of a circle. Geared to the learning needs of students in grades 5 through 8, these printable worksheets practice the subject pretty much across the board: easy, intermediate, and hard. The task in the simple theorem is to calculate the area and perimeter of circles with radius from 1 to 25. The middle set requires the answers to be rounded to the tenth place with a radius of 25 to 100. In the heavy worksheets, the radius is represented as a decimal and the task is to round your answers to two decimal places. Use pi = 3.14 wherever necessary. Explore some of these worksheets for free!

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Area and perimeter formulas are the two main formulas for any given two-dimensional shape in mathematics. In geometry, you will come across many shapes like circle, triangle, square, pentagon, octagon, etc. Also in real life you will come across different types of objects with different shapes and sizes occupying space in one place and their outline spacing indicates the overall length of the object.

All shapes have their own characteristics based on their structure, sides, and angles. The two main characteristics are area and perimeter. For example, the amount of paint needed to paint a rectangular wall is calculated based on its area, and to determine the boundaries of the square panel we need to calculate its perimeter to find the total length of the panel.

Every geometric shape has its area and perimeter. There are different formulas for the area and perimeter of each shape because they have different measurements. So let’s learn the area and perimeter formulas for all shapes here.

area formula

Area is the measure of the space enclosed by a closed geometric figure. Like the perimeter formula, there are a number of area formulas for polygons that can be represented using algebraic expressions.

For example, if you want to find the area of ​​a square box with sides 40 cm long, use the formula:

Area of ​​the square = a2, where a is the side of the square.

Similarly, the area of ​​a triangle can also be found using its area formula (1/2 × w × h).

perimeter formula

A perimeter is the length of the boundary of a closed geometric figure. Algebraic expressions can be used to represent the perimeter formula for the regular polygons. Suppose the side length of a regular polygon is l. The formula for the perimeter of the shapes for each of the polygons can be given using the same variable l.

Example: To find the perimeter of a rectangular box with a length of 6 cm and a width of 4 cm, we need to use the formula,

Perimeter of a rectangle = 2 (L+W) = 2 (6cm + 4cm) = 2 × 10cm = 20cm.

Area and perimeter formula chart

Area formulas for various geometric figures:

Numbers Area Formula Variables Area of ​​a rectangle Area = l × b l = Length w = Width Area of ​​a square Area = a2 a = Sides of the square Area of ​​a triangle Area = 1/ 2 b×h b = Base area h = Height Area of ​​a circle Area = π r2 r = radius of the circle area of ​​a trapezium area = 1/ 2 (a + b)h a = base 1 b = base 2 h = vertical height area of ​​the ellipse area = π ab a = radius of the major axis b = radius of the minor axis

Perimeter formulas for various geometric figures:

Geometric shape Perimeter Formula Metric Parallelogram 2 (base + height) Triangle a + b + c a, where b and c are the side lengths Rectangle 2 (length + width) Square 4a a = side length Trapezoid a + b + c + d a, b, c , d are the sides of the trapezoid kite 2a + 2b a = length of the first pair of equal sides b = length of the second pair of equal sides rhombus 4 x a a = length of one side hexagon 6 x a a = length of a side

Also read:

Area and perimeter of the special triangle

An equilateral triangle is a special triangle where all three sides are equal. To find its perimeter and area, we need to know all three sides of it.

Equilateral triangle

The perimeter of an equilateral triangle = 3 x side length = 3 l.

Area of ​​an equilateral triangle = √3 / 4 a2

Solved examples

Let’s see some examples using area and perimeter formulas:

Example 1: Find the perimeter of a rectangular box 6 cm long and 4 cm wide.

Solution: Use the formula

Perimeter of a rectangle = 2 (L+W) = 2 (6cm + 4cm) = 2 × 10cm = 20cm.

Example 2: How to find the area and perimeter of a square? Calculate the perimeter of a square if the area is 36 cm2.

Solution: A square is a shape where all four sides are the same length. These four sides are also parallel to each other. They also form an angle of 90° to each other. To find the area and perimeter of the square, we need to know the measurements of one side of the square.

Area of ​​a square = (side)2, and

Perimeter of a square = 4 (side)

Given: Area is 36 cm2

(side)2 = 36

Or Side = 6 (Negative value ignored since length cannot be negative)

Using the perimeter formula we have again

Circumference = 4 (side) = 4 x 6 = 24

So 24 cm is the perimeter of a square.

Area and perimeter is a very important topic in mathematics and students are advised to go through the list of formulas listed above before working on the problems for better understanding and preparation.

practice questions

Find the area of ​​a rhombus with a perimeter of 60 cm and one of its diagonals 24 cm. Calculate the area and perimeter of an equilateral triangle with side length 8 cm. A circular track runs around a circular park. If the difference between the perimeter of the track and the park is 66 m, find the width of the track.

Download BYJU’S-The Learning App and get personalized videos for all math concepts from grades 1 to 12.

what is a circle

A circle is a round figure that has no corners or edges.

In geometry, a circle can be defined as a closed, two-dimensional curved shape.

A few things around us that are circular are a car tire, a wall clock that tells the time, and a lollipop.

center of a circle

The center of a circle is the center in a circle from which all distances to points on the circle are equal. This distance is called the radius of the circle.

Here point P is the center of the circle.

Inside and outside of a circle

Consider the circle with center P and radius r. A circle has an inner and an outer area.

All points that are less than the radius of a circle lie inside the circle. For example, the points P, Q, and R are inside the circle.

All points whose distance is greater than the radius of a circle are outside the circle. For example, points S and T are on the outside of the circle.

All points whose distance is equal to the radius of a circle lie on the circle. For example, the points U and V lie on the circle.

semicircle:

Semi means half, so semicircle is semicircle. It is formed by slicing an entire circle along a line segment passing through the center of the circle. This line segment is called the diameter of the circle.

quadrant:

Quarter means a fourth. So a quadrant is a quadrant formed by dividing a circle into 4 equal parts or a semi-circle into 2 equal parts.

A quarter circle is also called a quadrant.

parts of a circle

The radius of a circle:

A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle.

Radius = $\frac{diameter}{2}$

diameter of a circle:

A segment that runs through the center of a circle and whose end points lie on the circle is called the diameter of the circle.

diameter = 2 × radius

Scope:

The circumference of a circle is the distance around a circle. It is the same as the scope of other shapes.

Chords of circles:

A segment whose endpoints lie on a circle is called a chord.

The diameter of a circle is its largest chord.

circular arc:

An arc is part of the circle with all its points on the circle. It’s a curve that’s part of its circumference.

An arc joining the endpoints of the diameter has a measure of 180° and is called a semicircle.

An arc divides the circle in two. The smaller part is called the secondary arc and the larger part is called the main arc.

The secant of a circle:

A secant is a straight line that intersects a circle at exactly two points.

Tangent of a circle:

A tangent is a straight line that intersects a circle at exactly one point.

Segments of a circle:

A chord divides the circular area into two parts. Each part is called the segment of the circle.

The segment containing the minor arc is called the minor segment, and the segment containing the major arc is called the major segment.

The sector of a circle:

The sector of a circle is a part of the circle enclosed by two radii and an arc of a circle as part of its boundary.

When two radii meet at the center of the circle to form the sector, it actually forms two sectors. A sector of a circle is called a minor sector if the minor arc of the circle is part of its boundary. A sector is called a major sector when the major arc of the circle is part of its boundary.

circular formulas

Area of ​​a circle:

The area of ​​a circle is the area enclosed within the circle.

The area of ​​a circle depends on the length of its radius.

Area = $\pi$r$^{2}$

Scope:

The distance around the circle is the circumference of the circle.

Circumference = 2$\pi$r

The value of $\pi$ = 3.14 or $\frac{22}{7}$

Solved examples on Circle

Example 1: Assign the correct definition to each term.

Solution:

1 – b

2 – T

3 – a

4 – c

Example 2: Use the figure to answer the questions.

Which term best describes OE? Name 3 line segments that have the same length. Name the secant. What two terms can be used to describe AB?

Solution:

Radius OA, OB and OE PQ diameter and chord

Example 3: If a circle has a radius of 3 cm, what is its longest chord?

Solution:

The longest chord is the diameter of the circle.

diameter = 2 × radius = 2 × 3 = 6 cm

Example 4: The minute hand of a round clock is 21 cm long. How far does the spike move in 1 hour?

Solution:

The distance traveled in 1 hour is the circumference of the clock, which is a circle.

Circumference = 2$\pi$r = 2 × $\frac{22}{7}$ × 21 = 132 cm

exercise problems

Circle Take this quiz and test your knowledge. 1 A circle with center O has radius 5 cm and OQ = 7 cm, where is point Q then? on the circle. Inside the circle. In the outside of the circle. True False The correct answer is: Outside the circle.

The length of OQ is greater than the radius of the circle. So the point Q lies outside the circle. 2 The total number of diameters of a circle is: 1 2 3 infinity (uncountable) True False Correct answer is: infinity (uncountable)

Diameter is the line segment that passes through the center of the circle and has endpoints on the circle. There are infinitely many straight lines that can go through a point, so there are infinitely many diameters of a circle. 3 Two circles with centers P and Q with radii 4 cm and 5.5 cm touch each other on the outside. What is the distance between their centers? 4 cm 5.5 cm 9.5 1.5 True False Correct answer is: 9.5

Distance between centers = 4 cm + 5.5 cm = 9.5 cm 4 If the circumference of the circle is 176 cm. What will his territory be? 56 cm2 2,464 cm2 232 cm2 1232 cm2 True False Correct answer is: 2,464 cm2

perimeter = 2πr

176 = 2 × $\frac{22}{7}$ × r

r = 28 cm

Area = πr2 = $\frac{22}{7}$ × 28 × 28 = 2,464 cm2

frequently asked Questions

A circle is an important shape in the field of geometry. Let’s look at the definition of a circle and its parts. We will also examine the relationship between the circle and the plane.

A circle is a shape where all points are the same distance from its center. A circle is named after its center. Therefore, the circle on the right is called circle A because its center is at point A. Some real world examples of a circle are a wheel, a dinner plate, and (the face of) a coin.

The distance on a circle through the center is called the diameter. A real world example of diameter is a 9 inch disk.

The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii in a row in a circle, they have the same length as a diameter. So the diameter of a circle is twice as long as the radius.

We can look at a pizza pie to find real world examples of diameter and radius. Look at the pizza on the right, cut down the middle into 8 equal pieces. A radius is formed by a straight line from the center to a point on the circle. A straight line that goes from one point on the circle and through its center to another point on the circle is a diameter. As you can see, a circle has many different radii and diameters, each passing through its center.

A chord is a line segment connecting two points on a curve. In geometry, a chord is often used to describe a line segment connecting two endpoints that lie on a circle. The circle on the right contains the AB chord. If this circle were a pizza pie, you could cut a slice of pizza along the AB chord. By cutting along the AB chord, you cut off a slice of pizza containing that chord.

It turns out that a diameter of a circle is the longest chord of that circle, since it goes through the center. A diameter satisfies the definition of a chord, but a chord is not necessarily a diameter. This is because every diameter goes through the center of a circle, but some chords do not go through the center. Thus it can be said that every diameter is a chord, but not every chord is a diameter.

Let’s look again at the definition of a circle. A circle is the set of points that are equidistant from a given point in the plane. The special point is the middle. In the circle on the right, the center is point A. So we have circle A.

A plane is a flat surface that extends in all directions without end. In the diagram on the right, plane P contains points A, B, and C.

Can you think of some real world objects that fit the definition of an airplane? It’s difficult at this mathematical level. Intuitively, you can think of an airplane as a flat, endless sheet of paper. The top of your desk and a blackboard are objects that can be used to represent a plane, although they don’t meet the definition above.

A circle divides the plane into three parts:

the points INSIDE the circle, the points OUTSIDE the circle, and the points ON the circle

You can see an interactive demonstration of this by hovering your mouse over the three items below.

A circle divides a plane into three parts:

the points INSIDE the circle, the points OUTSIDE the circle, and the points ON the circle

Example 1:

Name the center of this circle.

Answer: Point B

Example 2:

Name two chords on this circle that are not diameters.

Answer: DE and FG

Example 3:

Name all the radii on this circle.

Answer: BA, BC, BD and BG

Example 4:

What are AC and DG?

Answer: AC and DG are diameters.

Example 5:

If DG is 5 inches long, how long is DB?

Solution: The diameter of a circle is twice the radius.

5 inches ÷ 2 = 2.5 inches

Answer: The length of DB is 2.5 inches

Summary: A circle is a shape where all points are the same distance from its center. A circle is named after its center. The parts of a circle include a radius, a diameter, and a chord. All diameters are chords, but not all chords are diameters. A plane is a flat surface that extends in all directions without end. A circle divides the plane into three parts: the points inside the circle, the points outside the circle, and the points on the circle.

1. What is a chord but not a diameter?

PR

QA

pt

None of the above. RESULT BOX:

2. What is a radius?

pq

QR

QA

All of the above.

RESULT BOX:

3. Name the center of this circle.

point P

point Q

point R

None of the above. RESULT BOX:

4. What is PR (or PQR)?

diameter

radius

center

None of the above. RESULT BOX:

5. If PQ is 3 cm long, how long is PR?

video transcript

A candy machine produces small chocolate wafers in the form of round discs. The diameter of each wafer is 16 millimeters. What is the area of ​​each candy? So the candies, they say they’re in the shape of circular disks. And they tell us that the diameter of each wafer is 16 millimeters. If I draw a line across the circle that goes through the center, the length of that line across the entire circle through the center is 16 millimeters. So let me write this. The diameter here is 16 millimeters. And they want us to find out the area of ​​the surface of this candy, or essentially the area of ​​this circle. So if we think about area, we know that the area of ​​a circle is equal to pi times the radius of the circle squared. And you say, well, they gave us the diameter. what is the radius Well, you may remember that the radius is half the diameter. It is the distance from the center of the circle outwards, to the edge of the circle. So it would be that distance over here, which is exactly 1/2 the diameter, so 8 millimeters. So where we see the radius we could put 8 millimeters. So the area is equal to pi times 8 millimeters squared, which would be 64 square millimeters. And usually this is written with pi after 64. So you often see it as if this equals 64 pi millimeters squared. That’s the answer now, 64 pi millimeters squared. But sometimes just leaving it as pi isn’t that satisfying. You might say, well, I’d like to get an estimate of what number that’s close to. I want a decimal representation of it. And so we could start using approximate values ​​of pi. So the roughest approximation used is that pi, a very rough approximation, equals 3.14. So in this case we could say that this is equal to 64 by 3.14 square millimeters. And we can get our calculator to figure out what that’s going to be in decimal form. So we have 64 times 3.14 equals 200.96. So we could say that the area is roughly equal to 200.96 square millimeters. Now if we want to get a more accurate representation of this – pi actually just keeps going on and on and on – we could use the calculator’s internal representation of pi, in this case let’s say 64 times, and then we need to look up the pi in the calculator. It’s up here in this yellow, so I’m doing this little second feature. Get the Pi there. Each calculator will be a little different. But 64 times pi. And now we’re going to use the internal calculator approximation of pi, which will be more accurate than what I had in the last one. And you get 201 – so let me put it here so I can write it down – so more accurate is 201. And I’m going to round to the nearest hundred, so you get 201.06. So 201.06 square millimeters are more accurate. So this is closer to the actual answer, since a calculator’s representation is more accurate than this very rough approximation of what pi is.

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If you need to solve some geometry problems, this circumference calculator is the right site for you. It is a tool specially designed to find the diameter, circumference and area of ​​any circle. Read on to learn:

What is the definition of scope

How to find the circumference of a circle

How to convert circumference to diameter

Like all of our tools, the Circumference Calculator works both ways – it’s also a Circumference to Diameter Calculator and can be used to convert Circumference to Radius, Circumference to Area, Radius to Circumference, Radius to Diameter (duh!), Radius to area, diameter to perimeter, diameter to radius (yes, using rocket science again), diameter to area, area to perimeter, area to diameter, or area to radius.

If you want to draw a circle on the Cartesian plane, you might find this circle equation calculator useful.

video transcript

A candy machine produces small chocolate wafers in the form of round discs. The diameter of each wafer is 16 millimeters. What is the area of ​​each candy? So the candies, they say they’re in the shape of circular disks. And they tell us that the diameter of each wafer is 16 millimeters. If I draw a line across the circle that goes through the center, the length of that line across the entire circle through the center is 16 millimeters. So let me write this. The diameter here is 16 millimeters. And they want us to find out the area of ​​the surface of this candy, or essentially the area of ​​this circle. So if we think about area, we know that the area of ​​a circle is equal to pi times the radius of the circle squared. And you say, well, they gave us the diameter. what is the radius Well, you may remember that the radius is half the diameter. It is the distance from the center of the circle outwards, to the edge of the circle. So it would be that distance over here, which is exactly 1/2 the diameter, so 8 millimeters. So where we see the radius we could put 8 millimeters. So the area is equal to pi times 8 millimeters squared, which would be 64 square millimeters. And usually this is written with pi after 64. So you often see it as if this equals 64 pi millimeters squared. That’s the answer now, 64 pi millimeters squared. But sometimes just leaving it as pi isn’t that satisfying. You might say, well, I’d like to get an estimate of what number that’s close to. I want a decimal representation of it. And so we could start using approximate values ​​of pi. So the roughest approximation used is that pi, a very rough approximation, equals 3.14. So in this case we could say that this is equal to 64 by 3.14 square millimeters. And we can get our calculator to figure out what that’s going to be in decimal form. So we have 64 times 3.14 equals 200.96. So we could say that the area is roughly equal to 200.96 square millimeters. Now if we want to get a more accurate representation of this – pi actually just keeps going on and on and on – we could use the calculator’s internal representation of pi, in this case let’s say 64 times, and then we need to look up the pi in the calculator. It’s up here in this yellow, so I’m doing this little second feature. Get the Pi there. Each calculator will be a little different. But 64 times pi. And now we’re going to use the internal calculator approximation of pi, which will be more accurate than what I had in the last one. And you get 201 – so let me put it here so I can write it down – so more accurate is 201. And I’m going to round to the nearest hundred, so you get 201.06. So 201.06 square millimeters are more accurate. So this is closer to the actual answer, since a calculator’s representation is more accurate than this very rough approximation of what pi is.

The circumference is given by the formula C = πd, where π = 3.14 and d is the diameter of the circle.

explanation

The formula for the area of ​​a circle is A = πr2.

We are given the area and by substitution we know that 13π = πr2.

We divide the π and get 13 = r2.

We take the square root of r to find that r = √13.

We find the circumference of the circle with the formula C = 2πr.

We then plug in our values ​​to find C = 2√13π.