A childcare center has three playground areas: one square 32 feet on each side, one circular with a 30 feet diameter and one rectangular 30 feet wide and 45 feet long. To decrease injuries from falls, they want to spread recycled rubberized mulch to a depth of 6 inches. The mulch is $12.50 per cubic yard plus $25.00 delivery charge. How much will they pay for the mulch?

Given:

3 playground:

square = 32 feet per side

circle = 30 feet diameter

rectangle = 30 feet wide and 45 feet long

mulch = 6 inches

mulch costs 12.50 cubic yard plus 25 delivery charge.

Convert feet to yard: 1 yard = 3 feet

square = 32 feet * 1yard/3ft = 10.67 yards

diameter = 30 feet * 1yard/3ft = 10 yards

rectangle = 30 feet * 1yard/3ft = 10 yards; 45 feet * 1yd/3ft = 15 yards

convert inches to feet to yard: 1 foot = 12 inches; 1 yard = 3 feet

6 inches * 1ft/12 inches = 0.50 ft

0.50 ft * 1yd/3ft = 0.17 yards

square mulch = 10.67 yds * 10.67 yds * 0.17 yds = 19.35 cubic yards

circle = 3.14 * (5yds) ² * 0.17 yds = 13.35 cubic yards

rectangle = 10 yds * 15 yds * 0.17 yds = 25.50 cubic yards

19.35 yd³ + 13.35 yd³ + 25.50 yd³ = 58.20 yd³

58.20 yds³ * 12.50/yd³ = 727.50 cost of mulch

727.50 + 25 = 752.50

They will pay a total of $752.50 for the mulch.