Maths Circles Quiz Sections 1

Explanation
The correct answer is "radius." The radius of a circle is the distance from the center of the circle to any point on its circumference. It is represented by the letter "r" and is half the length of the diameter. The radius is an important measurement in determining the size and properties of a circle.

Explanation
The diameter of a circle is a line segment that passes through the center of the circle and connects two points on the circumference. It is twice the length of the radius. Therefore, the correct answer is "diameter" as it represents the measure of the line segment that passes through the center of the circle.

Explanation
The correct answer is 28.26. This is the area of the circle O.

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 18 inches, so the radius would be half of that, which is 9 inches. Plugging this value into the formula, we get A = π(9^2) = π(81) = 254.34 square inches. Therefore, the correct answer is 254.34.

Explanation
The area of a circle can be calculated using the formula A = πr², where r is the radius of the circle. In this case, the diameter is given as 38 cm, so the radius is half of that, which is 19 cm. Plugging this value into the formula, we get A = π(19)² = 1133.54. Therefore, the correct answer is 1133.54.

Explanation
The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. In this case, since the radius is not given, we cannot determine the exact circumference. Therefore, the given answer of 251.2 is not valid as there is not enough information provided to calculate the circumference.

Explanation
The circumference of a circle can be found by multiplying the diameter by pi (π). In this case, the diameter is given as 10 feet. Multiplying 10 by pi (approximately 3.14) gives us a result of 31.4. Therefore, the correct answer is 31.4.

Explanation
The given answer, 200.96, is the circumference of a circle. The circumference is the distance around the outer edge of a circle. In this case, a circle with a circumference of 200.96 units is being referred to.

Explanation
The minute hand of a clock moves in a circular motion. In one hour, it completes a full revolution around the clock face. The area covered by the minute hand can be calculated by finding the area of the sector it sweeps in that hour. The formula for the area of a sector is (θ/360) * π * r^2, where θ is the angle of the sector and r is the radius of the circle. Since the minute hand is 7 inches long, the radius is 7 inches. The angle of the sector is 360 degrees (a full revolution). Plugging these values into the formula, we get (360/360) * π * 7^2 = 1 * π * 49 = 153.86 square inches.

Explanation
To find the amount of sheet metal needed to cover the top and bottom of the tank, we need to calculate the area of two circles. The formula to find the area of a circle is A = πr², where r is the radius of the circle. In this case, the diameter of the circle is given as 8.5 feet, so the radius would be half of that, which is 4.25 feet.

Calculating the area of one circle: A = π(4.25)² = 56.72 square feet.

Since we need to cover both the top and bottom of the tank, we multiply this area by 2: 56.72 x 2 = 113.43 square feet.

Therefore, 113.43 is the amount of sheet metal needed to cover the top and bottom of the tank.