Circumference And Area Of A Circle Quiz

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.

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.

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.

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.

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.

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.

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.

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.