Circumference And Area Of A Circle Quiz

1. Round to the nearest tenth. Find the circumference of a circle with a radius of 5.6 meters.

98.5

35.2

36.8

18.5

The formula to find the circumference of a circle is C = 2πr, where r is the radius of the circle. In this case, the radius is given as 5.6 meters. Plugging in this value into the formula, we get C = 2π(5.6) = 11.2π. To round this to the nearest tenth, we need to find the value of π. Using the approximation 3.14 for π, we get C ≈ 11.2(3.14) = 35.168. Rounding this to the nearest tenth gives us 35.2. Therefore, the correct answer is 35.2.

Explanation

The formula to find the circumference of a circle is C = 2πr, where r is the radius of the circle. In this case, the radius is given as 5.6 meters. Plugging in this value into the formula, we get C = 2π(5.6) = 11.2π. To round this to the nearest tenth, we need to find the value of π. Using the approximation 3.14 for π, we get C ≈ 11.2(3.14) = 35.168. Rounding this to the nearest tenth gives us 35.2. Therefore, the correct answer is 35.2.

2. Round to the nearest tenth. Find the circumference of a circle with a radius of 30.9 centimeters.

194.1

2998.1

97.0

61.8

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 30.9 centimeters. Plugging this value into the formula, we get C = 2π(30.9) = 61.8π. To find the value of C rounded to the nearest tenth, we need to calculate the value of 61.8π and round it. The value of π is approximately 3.14. Multiplying 61.8 by 3.14, we get approximately 194.1. Therefore, the correct answer is 194.1.

Explanation

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 30.9 centimeters. Plugging this value into the formula, we get C = 2π(30.9) = 61.8π. To find the value of C rounded to the nearest tenth, we need to calculate the value of 61.8π and round it. The value of π is approximately 3.14. Multiplying 61.8 by 3.14, we get approximately 194.1. Therefore, the correct answer is 194.1.

3. Round to the nearest tenth. Find the area of a circle with a diameter of 6.8 meters.

36.3

36.4

145.2

145.1

To find the area of a circle, we can use the formula A = πr², where A is the area and r is the radius. In this case, we are given the diameter, which is twice the radius. So, we divide the diameter by 2 to find the radius. The diameter is 6.8 meters, so the radius is 6.8/2 = 3.4 meters. Now we can substitute the value of the radius into the formula to find the area. A = π(3.4)² = 36.316. Rounding to the nearest tenth, the area is 36.3.

Explanation

To find the area of a circle, we can use the formula A = πr², where A is the area and r is the radius. In this case, we are given the diameter, which is twice the radius. So, we divide the diameter by 2 to find the radius. The diameter is 6.8 meters, so the radius is 6.8/2 = 3.4 meters. Now we can substitute the value of the radius into the formula to find the area. A = π(3.4)² = 36.316. Rounding to the nearest tenth, the area is 36.3.

4. Round to the nearest tenth. A spinkler can spray water 10 feet in all directions. How much area can the sprinkler water?

62.8 sq.feet

36.3 sq.feet

314.0 sq.feet

98.9 sq.feet

The correct answer is 314.0 sq.feet. This can be calculated by using the formula for the area of a circle, which is πr^2. Since the sprinkler can spray water 10 feet in all directions, the radius of the circle is 10 feet. Plugging this value into the formula, we get π(10^2) = π(100) ≈ 314.0 sq.feet. Therefore, the sprinkler can water an area of approximately 314.0 sq.feet.

Explanation

The correct answer is 314.0 sq.feet. This can be calculated by using the formula for the area of a circle, which is πr^2. Since the sprinkler can spray water 10 feet in all directions, the radius of the circle is 10 feet. Plugging this value into the formula, we get π(10^2) = π(100) ≈ 314.0 sq.feet. Therefore, the sprinkler can water an area of approximately 314.0 sq.feet.

5. Round to the nearest tenth. Find the area of a circle with a diameter of 46.2 cm.

6702.1

1587.3

1675.5

145.1

The formula to find the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the diameter is given, so we need to divide it by 2 to find the radius. The radius is 46.2 cm / 2 = 23.1 cm. Plugging this value into the formula, we get A = π(23.1)^2. Rounding to the nearest tenth, the area is approximately 1675.5 square cm.

Explanation

The formula to find the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the diameter is given, so we need to divide it by 2 to find the radius. The radius is 46.2 cm / 2 = 23.1 cm. Plugging this value into the formula, we get A = π(23.1)^2. Rounding to the nearest tenth, the area is approximately 1675.5 square cm.

6. Round to the nearest tenth. Olivia used a stick to draw a circle in the sand. The circle was 4 meters in radius. How many square meters were inside the circle?

50.2

25.1

45.6

13.6

The correct answer is 50.2. To find the area of a circle, you use the formula A = πr^2, where A is the area and r is the radius. In this case, the radius is 4 meters. Plugging this into the formula, A = 3.14 × 4^2 = 3.14 × 16 = 50.24. Rounding to the nearest tenth, the answer is 50.2 square meters.

Explanation

The correct answer is 50.2. To find the area of a circle, you use the formula A = πr^2, where A is the area and r is the radius. In this case, the radius is 4 meters. Plugging this into the formula, A = 3.14 × 4^2 = 3.14 × 16 = 50.24. Rounding to the nearest tenth, the answer is 50.2 square meters.

7. Round to the nearest tenth. Find the area of a circle with a diameter of 25 yd.

157.0

256.3

490.6

503.1

To find the area of a circle, we use the formula πr², where r is the radius of the circle. The diameter is twice the radius, so we first divide the diameter by 2 to find the radius. Then, we square the radius and multiply by π to get the area. In this case, with a diameter of 25 yards, the radius is 12.5 yards. Squaring this gives us 156.25, which, when multiplied by π (approximately 3.14), gives us the area of approximately 490.625 square yards. Rounding this to the nearest tenth, we get 490.6 square yards.

Explanation

To find the area of a circle, we use the formula πr², where r is the radius of the circle. The diameter is twice the radius, so we first divide the diameter by 2 to find the radius. Then, we square the radius and multiply by π to get the area. In this case, with a diameter of 25 yards, the radius is 12.5 yards. Squaring this gives us 156.25, which, when multiplied by π (approximately 3.14), gives us the area of approximately 490.625 square yards. Rounding this to the nearest tenth, we get 490.6 square yards.

8. Round to the nearest tenth. What is the number of square meters of a half circle whose diameter is 8 m?

50.2

45.6

15.3

25.1

The correct answer is 25.1. To find the area of a half circle, we need to use the formula A = (πr²)/2, where r is the radius. The diameter is given as 8 m, so the radius is half of that, which is 4 m. Plugging the value of the radius into the formula, we get A = (π(4)²)/2 = 16π/2 = 8π. Rounding this to the nearest tenth, we get approximately 25.1.

Explanation

The correct answer is 25.1. To find the area of a half circle, we need to use the formula A = (πr²)/2, where r is the radius. The diameter is given as 8 m, so the radius is half of that, which is 4 m. Plugging the value of the radius into the formula, we get A = (π(4)²)/2 = 16π/2 = 8π. Rounding this to the nearest tenth, we get approximately 25.1.