Area Of A Circle Quiz Questions And Answers

1. The radius is always half of the diameter.

True

False

The statement is true because the radius of a circle is defined as the distance from the center of the circle to any point on its circumference. The diameter, on the other hand, is the distance across the circle passing through the center. Since the diameter spans the entire circle, it is always twice the length of the radius. Therefore, the radius is always half of the diameter.

Explanation

The statement is true because the radius of a circle is defined as the distance from the center of the circle to any point on its circumference. The diameter, on the other hand, is the distance across the circle passing through the center. Since the diameter spans the entire circle, it is always twice the length of the radius. Therefore, the radius is always half of the diameter.

2. A circle has a radius of 12 inches. What is the area of the circle?

400.14 inches squared

452.16 inches squared

75.36 inches squared

22.26 inches squared

To find the area of a circle, use the formula:

Area = π * r^2

where "r" is the radius of the circle.

Given:

Radius, r = 12 inches

Using the formula: Area = π * (12 inches)^2 Area = π * 144 square inches Area ≈ 3.14159 * 144 square inches Area ≈ 452.39 square inches

When rounded to two decimal places, the area is approximately 452.16 square inches.

Explanation

To find the area of a circle, use the formula:

Area = π * r^2

where "r" is the radius of the circle.

Given:

Radius, r = 12 inches

Using the formula: Area = π * (12 inches)^2 Area = π * 144 square inches Area ≈ 3.14159 * 144 square inches Area ≈ 452.39 square inches

When rounded to two decimal places, the area is approximately 452.16 square inches.

3. Molly is making pizza for supper and wants to cover the top of the pizza with sauce. She has measured the radius of the pizza to be 5 inches, how many square inches will the sauce cover?

31.4 inches squared

78.5 inches squared

15.7 inches squared

20 inches squared

The correct answer is 78.5 inches squared. To find the area of the top of the pizza that the sauce will cover, we need to calculate the area of a circle with a radius of 5 inches. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the given radius of 5 inches into the formula, we get A = π(5^2) = π(25) = 78.5 inches squared.

Explanation

The correct answer is 78.5 inches squared. To find the area of the top of the pizza that the sauce will cover, we need to calculate the area of a circle with a radius of 5 inches. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the given radius of 5 inches into the formula, we get A = π(5^2) = π(25) = 78.5 inches squared.

4. The diameter of a circle is 8 centimeters. What is the area?

50.24 centimeters squared

64 centimeters squared

16.24 centimeters squared

12 centimeters squared

Make sure you change the diameter to a radius. (divide by 2)

Explanation

Make sure you change the diameter to a radius. (divide by 2)

5. The radius of a circle is 3 inches. What is the area?

9.25 inches squared

20.28 inches squared

28.26 inches squared

34.22 inches squared

3 x 3 x 3.14

Explanation

3 x 3 x 3.14

6. What is the area of a circle with a diameter of 14 cm?

49π cm²

14π cm²

196π cm²

7π cm²

The area of a circle is calculated using the formula:

Area = πr²

where r is the radius of the circle.

In this case, the diameter is 14 cm, so the radius is 14 cm / 2 = 7 cm.

Substituting this value into the formula, we get:

Area = π(7 cm)² = 49π cm²

Explanation

The area of a circle is calculated using the formula:

Area = πr²

where r is the radius of the circle.

In this case, the diameter is 14 cm, so the radius is 14 cm / 2 = 7 cm.

Substituting this value into the formula, we get:

Area = π(7 cm)² = 49π cm²

7. Sam has baked a circular cake. The cake has a diameter of 10 inches. Sam needs to know how much icing it will take to cover the top of the cake; which of the following does Sam need to use to figure this out?

10 x 3.14

5 x 2 x 3.14

5 x 5 x 3.14

2 x 5 x 3.14

Area = radius x radius x pi

Explanation

Area = radius x radius x pi

8. A circular stool needs to be covered with new fabric. If the diameter of the stool is 2 feet, how much material is needed to cover the stool?

12.56 feet squared

6.28 feet squared

3.14 feet squared

7.22 feet squared

The correct answer is 3.14 feet squared. To find the amount of fabric needed to cover the circular stool, we need to calculate the area of the circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the diameter of the stool is given as 2 feet, so the radius is 1 foot. Plugging this value into the formula, we get A = 3.14 * 1^2 = 3.14 feet squared.

Explanation

The correct answer is 3.14 feet squared. To find the amount of fabric needed to cover the circular stool, we need to calculate the area of the circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the diameter of the stool is given as 2 feet, so the radius is 1 foot. Plugging this value into the formula, we get A = 3.14 * 1^2 = 3.14 feet squared.

9. The chord is the longest diameter in a circle.

True

False

The statement is false. A chord is a line segment that connects two points on a circle, but it does not have to pass through the center of the circle. The longest diameter in a circle is actually the line segment that passes through the center and has endpoints on the circle, also known as the diameter. Therefore, the chord is not the longest diameter in a circle.

Explanation

The statement is false. A chord is a line segment that connects two points on a circle, but it does not have to pass through the center of the circle. The longest diameter in a circle is actually the line segment that passes through the center and has endpoints on the circle, also known as the diameter. Therefore, the chord is not the longest diameter in a circle.

10. Pam's mom is fixing cookies for her class. She wants to put icing on the cookies. The radius of the cookies is 2 inches. She is making 20 cookies, what is the area that the icing will cover if she icings all 20 cookies?

251.2 inches squared

125.6 inches squared

12.56 inches squared

220 inches squared

The area of a circle can be found using the formula A = πr^2, where A is the area and r is the radius. In this case, the radius of each cookie is given as 2 inches. So, the area of one cookie is A = π(2)^2 = 4π square inches. Since she is making 20 cookies, the total area that the icing will cover is 20 times the area of one cookie, which is 20 * 4π = 80π square inches. Approximating π as 3.14, the total area is approximately 251.2 square inches.

Explanation

The area of a circle can be found using the formula A = πr^2, where A is the area and r is the radius. In this case, the radius of each cookie is given as 2 inches. So, the area of one cookie is A = π(2)^2 = 4π square inches. Since she is making 20 cookies, the total area that the icing will cover is 20 times the area of one cookie, which is 20 * 4π = 80π square inches. Approximating π as 3.14, the total area is approximately 251.2 square inches.