A sandpit in the shape of a rectangular prism has length 7 feet, width 5 feet, and height 1.75 feet. It is filled to the brim with sand. Joe puts this sand into a second sandpit having the same shape but a larger base. He needs 17.5 cubic feet of sand to fill the extra space inside the second sandpit.

Question

A sandpit in the shape of a rectangular prism has length 7 feet, width 5 feet, and height 1.75 feet. It is filled to the brim with sand.  Joe puts this sand into a second sandpit having the same shape but a larger base.  He needs 17.5 cubic feet of sand to fill the extra space inside the second sandpit.

If the height of the two sandpits is the same, what are the dimensions of the base of the second sandpit?
Answer
A. 5 feet x 2 feet
B. 10 feet x 7 feet
C. 9 feet x 5 feet
D. 20 feet x 25 feet

Luismiguel · Answer

You have:
lxWxh= volume of a square prism
So...

1.75ft X 5ft X 7ft= 61.25
+17.5( what the kid is missing)

78.75(sum)=(1.75ft)l x W
45=l x W

Proportions:
7ft/35ft=x/45ft= l = 9ft
Then do the same for the width and you get that the final answer is
C. 9ft x 5ft