i don't understand this question

Question

Consider the diagram of the basketball fitting perfectly into the box it comes in. If the volume of the ball is approximately 904.32 in³, what is the height of the box to the nearest inch? Use 3.14 for pi.

Answer 1

Hi Lakshya,

It sounds like this question is asking how tall a box would be if the basketball described fit perfectly inside it. This would mean the diameter of the ball is the same as the height of the box.

We can use the formula of the volume of a sphere to find the diameter.

V = (4/3)π r³

We know the volume is 904.32 in³ and we will use 3.14 as the value of π.

904.32 = (4/3)*(3.14) r³

Mulityply

904.32 = 4.19 r³

Divide both sides by 4.19

215.83 = r³

Take the cube root of each side

r = 6; so the radius is 6in.

If the radius is 6 inches, the diameter is 12 inches. So the box being described should be 12 inches tall.