Answer:
Step-by-step explanation:
What do we know about that prism?
It's a rectangular prism with a square base.
Height: y (from question)
base length: x (from question)
base width: x (from question, since it's a square base).
Total volume: 150 cu inches
The question lacks a relationship between x and y the "is __ times", but we can see from the answer choices that they all show a constant relationship:
y = 1.5 x
The volume of a prism is obtained by multiplying the lengths of its 3 dimensions: V = length * width * height. In our case, we then have
150 = x * x * y
then we replace y by its x-expressed equivalent:
150 = x * x * (1.5x) = 1.5x³
then we isolate x³ by dividing each side by 1.5
x³ = 100, we do the cubic root on each side
x = 4.64
So, answer is D. x = 4.6 and y = 6.9
If you you 4.64 * 4.64 * 6.96 = you get 149.8, which is very close to 150.
