Question

The basketball shown is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the basketball. What is the surface area and the volume of the box?

Answer 1

SA = 6 (edge X edge)

Volume of a cube = edgae x edge x edge

Answer 2

The surface area and volume of the cube are 5400 in² and 27,000 in³.

Explanation:

We are given that the volume of the cube is 4500π in³.

As, Volume of a cube =
`(4)/(3)\pi r^3`

So, we have,

`4500\pi = (4)/(3)\pi r^3\\\\r^3=(4500* 3)/(4)\\\\r^3=3375\\\\r=15\ inches`

Then, the diameter (d) is given by,

`d=2r\\\\d=2* 15\\\\d=30\ inches`

Since, the diameter of the basketball is equal to the edge length of the cube.

Then, edge length of the cube (a) is 30 inches.

So, Surface area of the cube =
`6a^2=6* 30^2=5400\ in^2`

And, Volume of the cube =
`a^3=30^3=27000\ in^3`

Hence, the surface area and volume of the cube are 5400 in² and 27,000 in³.