Question

Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box (y) is 1 1/2 times the base length of the box (x). Find the approximate height and the length of the box.

the pic is the answer choices

Answer 1

volume of square based prism = a²h
therefore
150 in³ = x²y
y = 1.5x
150 = 1.5x³
100 = x³
x = ³√100 ≈ 4.64 in
y = 1.5x ≈ 6.96 in

therefore 4th option is correct

Answer 2

Answer:

x = 4.6 and y = 6.9

Step-by-step explanation:

Box = Prism Shape = square base (Given)

Volume = 150 in³ (Given)

Equation of volume =  V = s²h  

= 150 = s²h  

Height of the box = 3/2 times the base length, thus -  

= h = (3/2)s  

Substituting the value into the volume equation, and solving for s -

= 150 = s²h  

= 150 = s²(3/2)s  

= (2/3)150 = s³  

= 100 = s³  

s = ∛100 (approx 4.642 in)  

Now since we the value for s, we can solve for h -

h = (3/2)∛100 (approx 6.962 in)

Therefore, the approximate height and the length of the box is x = 4.6 and y = 6.9