Question

In the following figure, the base of the pyramid has the same area as the base of the cylinder, and the cylinder is twice the height of the pyramid. What is the ratio of the volume of the pyramid to the volume of the cylinder?

• A. $1$ to $3$
• B. $1$ to $6$
• C. $2$ to $3$
• D. $3$ to $2$
• E. $6$ to $1$

Answer 1

The correct option is B $1$ to $6$

The area of base of cylinder$\left(a\right)$ is equal to the base of pyramid$\left(b\right)$

The height of cylinder$\left(h\right)$ is twice the height of pyramid$\left(p\right)$

Given $a=b$ and $h=2p$

The volume of pyramid is $\frac{1}{3}ah$

The volume of cylinder is $bp=2ah$

So the ratio of volumes is $\frac{1}{6}$

Therefore the correct option is $B$