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

Answer:

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

Step-by-step explanation:

Answer 2

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

so

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to    

$V=\pi r^{2}h$

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$    

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$    

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter    

$h=4*r=4*1.5=6\ in$  

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$  

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is  $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

the answer is the option

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