Question

Alana makes soup and packages it in conical containers that each have a height of 5 inches. What is the radius of each container of a pack of 12 containers contains 203.5 inches of soup? Use 3.14 to represent pi and round to the nearest tenth

Answer 1

We are given that 12 cones contain 203.5 cubic inches. Since there a re 12, the volume of each individual cone is:

`V=(203.5in^3)/(12)=16.96in^3`

Now, the volume of a cone is given by the following formula:

`V=(1)/(3)\pi r^2h`

Where "r" is the radius and "h" the height. Solving for the radius first by multiplying by 3:

`3V=\pi r^2h`

Now we divide both sides by pi:

`(3V)/(\pi)=r^2h`

Now we divide both sides by "h":

`(3V)/(\pi h)=r^2`

Now we take the square root to both sides:

`\sqrt[]{(3V)/(\pi h)}=r`

Now we replace the known values:

`\sqrt[]{(3\mleft(16.96in^3\mright))/(\mleft(3.14\mright)\mleft(5in\mright))}=r`

Solving the operations:

`\sqrt[]{(50.88in^2)/(15.7)}=r`
`\sqrt[]{3.2in^2}=r`
`1.8in=r`

Therefore, the radius is 1.8 inches.