Question

Rachel had 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 of the box (x). Find the approximate height and the length of the box

Answer 1

Let

x--------> the length side of the square base of the box

y-------> the height of the box

V------> volume of the box

we know that

V=x²*y

V=150 in³

so

150=x²*y------> equation 1

y=1.5*x------> equation 2

substitute the equation 2 in equation 1

150=x²*[1.5*x]-----> x³=150/1.5------> x³=100

x=4.64 in

y=1.5*4.64-----> y=6.96 in

therefore

the answer is

the length side of the square base of the box is 4.64 in

the height of the box is 6.96 in