Question

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?

Answer 1

The answer is $738.

Explanation:

The center has one square 32 feet on each side.

One circular playground with a 30 feet diameter.

One rectangular playground 30 feet wide and 45 feet long.

The center people are putting the mulch to a depth of 6 inches or 0.5 feet.

We have to find the volumes of all grounds:

The volume of the square playground is
`32*32*0.5 =512` ft³

The volume of the circular playground is
`3.14*15*15*0.5=353.25` ft³

The volume of the rectangular playground is
`30*45*0.5= 675` ft³

So the total volume of rubber needed =
`512+353.25+675=1540.25` ft³

The given price is in yards so 1 cubic yard is equal to 27 cubic feet.

So, for 3 feet per yard the volume of rubber is =
`1540.25/27=57.04` yard³

Given price is $12.50 per cubic yard so, for 57.04 cubic yards, the price will be:

`12.50*57.04=713` dollars

Adding the delivery cost of $25.

The grand total is
`713+25=738`dollars

Hence, the answer is $738.

Answer 2

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.