Question

rachel has a box in the shape of a rectangular prism the length of the box is 3 feet the width is 1.5 feet, and the height is 1 foot. what is the volume of the box measured in cubic inches ?

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

Answer 2

Answer:

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.