Question

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.

a)$740
b)$1,310
c)$8,575
d)$25,750

Answer 1

Volume= length*width*height = Area * height 
square region: A= 32^2= 1024 
circle region: A= pi*radius^2= pi*(diameter/2)^2= 15^2 pi= 225pi 
rectangle region: A= 30*45= 1350 
Volume= (1024+ 1350 +225pi) *6 = 14,244 +1350pi 
The units are ft^3 
1 yard = 3 feet 
yard^3= 27 ft^3 
ft^3= 1/(27y^3) 
Cost = price / unit *Volume +surcharge 
Cost= 12.50/y^3 *(14,244 +1350pi)ft^3 +25 
= 12.50/27 *(14,244 +1350pi) +25 
~ $8583