Question

Find the total volume of ice cream in the picture below. The cone is filled with ice cream as well. Assume the visible ice cream is a hemisphere. Round answer to the nearest hundredth. No pi in your answer.

Answer 1

We have a cone and a hemisphere

First, we will calculate the volume of the cone, the formula is

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

where r is the radius and h is the height

in our case

h=24

r=14/2=7

we substitute the values

`V_c=(1)/(3)\pi(7)^2(24)=1231.5`

Then we will calculate the volume of the hemisphere, the formula is

`V_H=(2)/(3)\pi r^3`

where r is the radius

in our case

r=7

`V_H=(2)/(3)\pi(7)^3=718.38`

Then in order to have the total volume of the ice cream, we need to sum the volumes that we calculated previously

`V=V_c+V_H`
`V=1231.5+718.38=1949.88`