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.
Answer:
The answer is $738.
Step-by-step 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 @@MATH_TOKEN_0@@ ft³
The volume of the circular playground is @@MATH_TOKEN_1@@ ft³
The volume of the rectangular playground is @@MATH_TOKEN_2@@ ft³
So the total volume of rubber needed = @@MATH_TOKEN_3@@ 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 = @@MATH_TOKEN_4@@ yard³
Given price is $12.50 per cubic yard so, for 57.04 cubic yards, the price will be:
\(12.50\times57.04=713\) dollars
Adding the delivery cost of $25.
The grand total is @@MATH_TOKEN_6@@dollars
Hence, the answer is $738.
