Question

How does the volume of a cone compare to the volume of a cylinder with the same radius and height?

one-third of the volume
one-half of the volume
twice the volume
triple the volume

Answer 1

one-third of the volume

Explanation:

`\text{The formula of volumes of:}\\\\a\ cone:\ V_(cone)=(1)/(3)\pi r_1^2H_1\\\\a\ cylinder:\ V_(cylinder)=\pi r_2^2H_2\\\\\text{If cone and cylinder are with the same radius and height, then:}\\\\r_1=r_2=r\ \text{and}\ H_1=H_2=H\\\\V_(cone)=(1)/(3)\pi r^2H,\ V_(cylinder)=\pi r^2H\to V_(cone)=(1)/(3)V_(cylinder)`