# Math Help - advanced geometry volume problems

1. ## advanced geometry volume problems

A cyndrilical cake has a 50 degree slice removed from it. the cake is 9 inches high and has a radius of 3 inches. what is the volume of the remaining cake?

A circular piece of paper has a 90 degree sector removed from it. It is the rolled up into a cone. If the radius of the initial circle is 8 inches, what will be the volume of this resulting cone to the nearest cubic inch?

2. For the first problem I would just take the volume of the whole cake, $9\pi 3^2$ and multiply it by the required ratio. which is
$\frac{360}{360}-\frac{50}{360}=\frac{31}{36}$.

For the second problem you know that the circumference of the circle is $2\pi r$ and the slant height of the cone will equal the radius of the circle. So the circumference of the base of the cone will be $\frac{3}{4}$ of the circle's circumference. From that you can work out the radius of the cone. Since it is a right cone with it's vertex over the centre of it's base the equation relating it's radius, height and slant height is $s=\sqrt{r^2+h^2}$. From that you can work out the height. Then, knowing the height and the radius, you can calculate the volume of the cone.