Precalculus problem

Question

The height of a cylinder is two times the diameter. Write the volume of the cylinder as a function of its radius.

Answer 1

Volume = height times area of horizontal cross section of the cylinder

V=h(pi)r² Area of the cross section is the area of a circle.

height = 2 diameter = 2(2r)=4r

V=4r(pi)r²

V=4(pi)r³