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

$V_c=\frac{1}{3}\pi r^2h$

where r is the radius and h is the height

in our case

h=24

r=14/2=7

we substitute the values

$V_c=\frac{1}{3}\pi(7)^2(24)=1231.5$

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

$V_H=\frac{2}{3}\pi r^3$

where r is the radius

in our case

r=7

$V_H=\frac{2}{3}\pi(7)^3=718.38$

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$