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 $7.50 per linear foot. About how much will the fencing cost altogether? Round to the nearest hundredth. Use 3.14 for π.

$693.90

Step-by-step explanation:

If the diameter is 36 ft, we can find the circumference, which is the distance around the garden

C = pi * d

C = 3.14 * 36

C =113.04 ft

Semicircular means 1/2, so divide by 2

113.04/2 =56.52

Add the fence across the diameter part = 36

56.52 +36=92.52

It costs 7.50 per foot

Take the circumference times the cost per foot

92.52*7.5 =$693.90

First, we need the circumference, using dπ. That means the total circumference is 36π, so the semi-circle's circumference is 18π. Then, we add the cross-section, meaning we add 36.

So, the perimeter is 18π + 36. Substituting π, we get 56.52 + 36 = 92.52.

Then we multiply by $7.50 giving us $693.90.

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