Question

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism. The company wants to use the package that has the least amount of wasted space. The company should choose the prism because it has approximately 11.6 in.3 less wasted space than the cylinder. the prism because it has approximately 14.1 in.3 less wasted space than the cylinder. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism. the cylinder because it has approximately 14.1 in.3 less wasted space than the prism.

Answer 1

1. Consider the 2 pictures attached below.

2. "The company wants to use the package that has the least amount of wasted space. "
"least space" means that the company wants the minimum volume possible to pack the ball.

3. Consider the cylinder. Volume=
`\pi r^(2) *height= \pi r^(2) *2r=2 \pi r^(3)` (in cubed), approximately
`2 *3.14r^(3)=6.28r^(3)`

the volume of the cube box is V=
`(2r)^(3)=8r^3`

4. The volume of the sphere is
`(4)/(3) \pi r^(3)= (4)/(3) (3.14) r^(3)=4.2r^(3)` in^3

The wasted space in the cylinder is
`6.28r^(3)-4.2r^(3)=2.08*r^(3)=2.08*(1.5)^(3)=7.02` in^3

The wasted space in the prism box is
`8r^(3)-4.2r^(3)=3.8r^(3)=3.8*(1.5)^(3)=12.825`

The company should chose the cylinder box because it has approximately 5.8 (inch cubed) less wasted space than the prism box.

Answer 2

C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

Explanation:

if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.