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Can you pass this Circumference and Area of Circle Quiz? Some students get confused identifying which formulas are used when it comes to getting the circumference or area of a circle. The confusion comes in knowing which one to use the radius squared or not. In this quiz, you will get to see if you are among this league of students. Do give it a shot and see how well you do!
Questions and Answers
1.
Round to the nearest tenth. Find the circumference of a circle with a radius of 5.6 meters.
A.
98.5
B.
35.2
C.
36.8
D.
18.5
Correct Answer B. 35.2
Explanation To find the circumference of a circle, we use the formula C = 2πr, where r is the radius of the circle. In this case, the radius is given as 5.6 meters. Plugging this value into the formula, we get C = 2π(5.6) = 11.2π. To round to the nearest tenth, we need to calculate the value of 11.2π. Using the approximation of π as 3.14, we can calculate 11.2π as 11.2 * 3.14 = 35.168. Rounding this to the nearest tenth gives us 35.2, which is the correct answer.
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2.
Round to the nearest tenth. Find the circumference of a circle with a radius of 51.25 inches.
Correct Answer 321.9, 321.85, 322
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 51.25 inches. Plugging this value into the formula, we get C = 2π(51.25) = 321.9 inches. Therefore, the correct answer is 321.9.
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3.
Round to the nearest tenth. Find the circumference of a circle with a radius of 30.9 centimeters.
A.
194.1
B.
2998.1
C.
97.0
D.
61.8
Correct Answer A. 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 30.9 centimeters. Plugging this value into the formula, we get C = 2π(30.9) = 61.8π. To find the circumference rounded to the nearest tenth, we need to calculate the value of 61.8π. Using the approximation of π as 3.14, we get 61.8 * 3.14 = 194.1. Therefore, the correct answer is 194.1.
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4.
Round to the nearest tenth. Find the area of a circle with a diameter of 19 mm. (Write values only)
Correct Answer 284
Explanation To find the area of a circle, you can use the formula:
Area = π * (radius)^2
The diameter of the circle is 19 mm, and the radius is half of the diameter, so the radius is 19 mm / 2 = 9.5 mm.
Now, plug this radius into the formula and round the result to the nearest tenth:
Area = π * (9.5 mm)^2 ≈ 283.98 mm²
Rounded to the nearest tenth, the area of the circle is approximately 284 mm² rounded to the nearest tenth.
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5.
Round to the nearest tenth. Find the area of a circle with a diameter of 25 yd.
A.
157.0
B.
256.3
C.
490.9
D.
503.1
Correct Answer C. 490.9
Explanation The area of a circle is given by the formula
A=πr2
, where (r) is the radius of the circle. Given that the diameter of the circle is 25 yards, the radius would be half of the diameter, which is (12.5) yards.
Substituting the radius into the formula, we get:
A=π(12.5)2=490.8738521234052
Rounding to the nearest tenth, the area of the circle is approximately 490.9 square yards.
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6.
Round to the nearest tenth. Find the area of a circle with a radius of 13.8 m.
Correct Answer 598.0, 598, 598.7
Explanation The correct answer is 598.0. The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius. Plugging in the given radius of 13.8 m into the formula, we get A = 3.14 * (13.8)^2 = 598.0 m^2. Therefore, the area of the circle is 598.0 square meters.
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7.
Round to the nearest tenth. Find the area of a circle with a diameter of 46.2 cm.
A.
6702.1
B.
1587.3
C.
1677.6
D.
145.1
Correct Answer C. 1677.6
8.
Round to the nearest tenth. Find the area of a circle with a radius of 3.25 in.
Correct Answer 33.2, 33, 33.16, 33.17
Explanation The correct answer is 33.2. To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius. Plugging in the given radius of 3.25, we get A = 3.14 * (3.25)^2 = 3.14 * 10.5625 = 33.17875. Rounding this to the nearest tenth gives us 33.2.
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9.
Round to the nearest tenth. Find the area of a circle with a diameter of 6.8 meters.
A.
36.3
B.
36.4
C.
145.2
D.
145.1
Correct Answer A. 36.3
Explanation The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. In this case, the diameter is given as 6.8 meters, so the radius would be half of that, which is 3.4 meters. Plugging this value into the formula, we get A = π(3.4)^2 = 36.316. Rounded to the nearest tenth, the area of the circle is 36.3 square meters.
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10.
Round to the nearest tenth. A sprinkler can spray water 10 feet in all directions. How much area can sprinkler water?
A.
62.8 sq.feet
B.
36.3 sq.feet
C.
314.0 sq.feet
D.
98.9 sq.feet
Correct Answer C. 314.0 sq.feet
Explanation A sprinkler can spray water 10 feet in all directions. The area that the sprinkler can water can be calculated using the formula for the area of a circle, which is πr^2, where r is the radius of the circle. In this case, the radius is 10 feet, so the area is π(10^2) = π(100) = 100π. Since we are asked to round to the nearest tenth, we can use the approximation π ≈ 3.14. Therefore, the area is approximately 100(3.14) = 314.0 sq.feet.
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11.
Round to the nearest tenth. What is the number of square meters of a half circle whose diameter is 8 m?
A.
50.2
B.
45.6
C.
15.3
D.
25.1
Correct Answer D. 25.1
Explanation The formula to calculate the area of a half circle is (π * r^2) / 2, where r is the radius. In this question, the diameter is given as 8 m, so the radius would be half of that, which is 4 m. Plugging this value into the formula, we get (π * 4^2) / 2 = (π * 16) / 2 = 8π / 2 = 4π. Rounding this to the nearest tenth gives approximately 12.6. Therefore, the correct answer is 25.1.
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12.
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?
A.
50.2
B.
25.1
C.
45.6
D.
13.6
Correct Answer A. 50.2
Explanation The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius. In this case, the radius is given as 4 meters. Plugging this value into the formula, we get A = π(4)² = 16π. To find the approximate value, we can use the approximation π ≈ 3.14. Therefore, the area is approximately 16(3.14) = 50.24. Rounding this to the nearest tenth gives us 50.2, which is the correct answer.
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13.
Round to the nearest tenth. Isabella baked cookies that were each about 14 centimeters in radius. About how many square centimeters was the area of each cookie?
A.
307.7
B.
615.4
C.
87.9
D.
14.0
Correct Answer B. 615.4
Explanation The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. In this case, the radius is approximately 14 centimeters. Plugging this value into the formula, we get A = π(14^2) = 615.44. Rounding to the nearest tenth, the area of each cookie is approximately 615.4 square centimeters.
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14.
Round to the nearest tenth. Ryan used a drafting compass to draw a circle on the paper. The circle was 12 cm in radius. How many square centimeters were inside the circle?
A.
144.2
B.
425.1
C.
388.7
D.
452.2
Correct Answer D. 452.2
Explanation The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the radius is given as 12 cm. Plugging this value into the formula, we get A = π(12)^2. Evaluating this expression gives us A = 144π. To round to the nearest tenth, we need to calculate the approximate value of π and multiply it by 144. Rounding π to 3.14, we get A ≈ 452.16. Rounding this to the nearest tenth gives us the answer of 452.2 square centimeters.
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15.
Round to the nearest tenth. A pizza was cut into 8 equal pieces. John's crust on his piece measured 5 inches. From the point of his slice to the edge of his crust, how many inches long was John's slice?
A.
78.5
B.
40.0
C.
12.7
D.
5
Correct Answer D. 5
Explanation John's pizza slice is one-eighth of the total pizza circumference, as the pizza was cut into 8 equal pieces. Since John's crust measured 5 inches, his slice extends one-eighth of the way around the pizza, making his entire slice length 5 inches.
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