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 1.5 times the base length of the box (x). Find the approximate height and the length of the box

Answer 1

Answer: The length of box is 5 inches.

Height of prism is 7 inches

Step-by-step explanation:

Let the base length of box be 'x'.

Let the height of box be 1.5x

Since we have given that

Volume of box = 150 cubic inches

Base of prism is in the shape of square.

So, Area of base of prism = Side × Side = x²

As we know the formula for "Volume of prism":

Volume = Area of base of box × Height

$150=x^2\times 1.5x\\\\150=1.5x^3\\\\\dfrac{150}{1.5}=x^3\\\\100=x^3\\\\x=4.64\ inches$

Hence, the length of box is 4.6 ≈ 5 inches.

Height of prism is 1.5x =1.5×4.6 =6.9 ≈ 7 inches

Answer 2

X*x*1.5x = 150 
1.5x³ = 150 
x³ = 100 

x = 4.641588834 

x ≈ 4.6 and y ≈ 6.9 <-----