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
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
To find the dimensions of the base of the second sandpit, we need to consider the difference in volume between the two sandpits.
The first sandpit has a volume of 7 feet x 5 feet x 1.75 feet = 61.25 cubic feet.
The second sandpit has a volume of the first sandpit plus the extra 17.5 cubic feet of sand, which is 61.25 cubic feet + 17.5 cubic feet = 78.75 cubic feet.
Since the height of the two sandpits is the same, the volume is determined by the base dimensions.
To find the base dimensions, we can rearrange the formula for volume of a rectangular prism:
Volume = length x width x height
Given that the height is the same for both sandpits, we can rewrite the formula as:
Volume / height = length x width
For the first sandpit, this gives us:
61.25 cubic feet / 1.75 feet = 35 feet x width
Simplifying this, we find:
35 feet x width = 61.25 cubic feet / 1.75 feet
width = (61.25 cubic feet / 1.75 feet) / 35 feet
width ≈ 1.75 feet
Since the width of the second sandpit is larger than the width of the first sandpit, we know that the base dimensions of the second sandpit must be greater than 5 feet x 1.75 feet.
Comparing the given answer choices, we find that the only option with a larger width is 10 feet x 7 feet, so the correct answer is B. 10 feet x 7 feet.