Question

A museum groundskeeper is creating a semicircular statuary garden with a diameter of 36 feet. There will be a fence around the garden. The fencing costs $7.25 per linear foot. About how much will the fencing cost altogether? Round to the nearest hundredth. Use 3.14 for π.

Answer 1

The fencing will cost about $740.16.

Explanation:

Find how much fencing is needed around the garden by finding the perimeter of the semicircular garden. To find the perimeter of a semicircle, add half of the circumference of the circle to the diameter of the circle.

P = 1 / 2 πd + d Use the circumference formula and divide it by 2 because the garden is a semicircle. Add the diameter to take into account all sides of the semicircle.

P ≈ 3.14(36) /2 + 36 Substitute for the diameter and π.

P ≈ 92.52 Simplify.

The perimeter of the semicircular garden is about 92.52 feet, therefore the fence will be 92.52 feet long.

Find how much the fencing will cost altogether. Multiply the length of the fence by the cost per linear foot of the fencing.

92.52 × 8.00 = 740.16