Volume of Cylinders, Cones, Spheres flashcards

Question 1

State the volume formula for a cylinder with radius $r$ and height $h$.

Accepted Answer

$$V=\pi r^2 h$$ where $r$ is the base radius and $h$ is the perpendicular height.

Question 2

Compute the volume of a cone with $r=6$ and $h=9$.

Accepted Answer

$$V=\frac{1}{3}\pi(6)^2(9)=108\pi\ 	ext{units}^3$$

Question 3

A cylinder has $r=4$ and $h=12$. A cone with the same $r$ and $h$ is removed from it. What is the remaining volume?

Accepted Answer

Cylinder: $V=\pi(4)^2(12)=192\pi$. Cone removed: $\frac{1}{3}(192\pi)=64\pi$. Remaining: $192\pi-64\pi=128\pi\ 	ext{units}^3$.

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