Question

The volume of a cone is 20pi cubic meters. What is the volume of a cylinder with the same base and height?

Answer 1

Recall, the volume of a cone is 1/3pi times radius of base times height.
$V cone_{} = \frac{1}{3} * \pi *r^2*h$

Volume of a cylinder is the same but without the 1/3
$V cyl_{} = \pi*r^2*h$

It gives you the cone volume 20pi and that the radius and height of both of them are the same values.
$20 \pi= \frac{1}{3} \pi r^2h$
$V cyl_{}= \pi r^2h$

since it says the radius and height are the same for both , you can equate the two, you can solve both equations for r^2*h and then equate what is on the other side.
$60=r^2h$
$\frac{V}{ \pi } =r^2h$

so
$60= \frac{V}{ \pi }$
$V=60 \pi$