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

The small pit used 35*1.75 ft^3 of sand

The large pit used all that plus an addition 17.5 = 10*1.75 ft^3

35*1.75
+10*1.75
----------
45*1.75

Looks like (C) to me.

To find the dimensions of the base of the second sandpit, we need to determine the volume of the original sandpit and then subtract the volume of the sandpit filled with sand.

The volume of a rectangular prism is found by multiplying its length, width, and height.

For the original sandpit:
Volume = length x width x height
Volume = 7 feet x 5 feet x 1.75 feet
Volume = 61.25 cubic feet

Next, we subtract the 17.5 cubic feet of sand that Joe adds to the second sandpit from the original volume to find the volume of the empty space in the second sandpit.

Empty space volume = original volume - added sand volume
Empty space volume = 61.25 cubic feet - 17.5 cubic feet
Empty space volume = 43.75 cubic feet

Since the height of the two sandpits is the same, the dimensions of the base of the second sandpit will be the same as the original sandpit, but with a larger volume to accommodate the 43.75 cubic feet of empty space.

To find the dimensions of the base, we need to calculate the area of the base and then divide the empty space volume by the calculated area.

Area of the base = length x width
Area of the base = 7 feet x 5 feet
Area of the base = 35 square feet

To find the dimensions of the base of the second sandpit, we divide the empty space volume by the area of the base:

Dimensions of the base = Empty space volume / Area of the base
Dimensions of the base = 43.75 cubic feet / 35 square feet

Calculating this division, we find that the dimensions of the base of the second sandpit are approximately 1.25 feet x 1.25 feet.

Thus, the correct answer is not provided among the answer choices.