Question 41·Medium·Geometry and Trigonometry

The problem gives the diameter of the base. How do you find the radius from the diameter?

Once you have the radius and the height, plug them into $V = \pi r^2 h$ and simplify carefully. Pay attention to squaring the radius and to the order of multiplication.

In a Desmos expression line, type 8/2 to verify that the radius is 4 centimeters.

In a new expression line, type pi*(4^2)*9. Desmos will show a decimal approximation and may also display an exact expression of the form (number)*pi; the number multiplying pi is the volume in cubic centimeters that matches one of the answer choices.

For a right circular cylinder, the volume formula is $V = \pi r^2 h$, where $r$ is the radius of the circular base and $h$ is the height of the cylinder. We are given the height $h = 9$ cm and the base diameter, not the radius.

The diameter of the base is 8 cm. The radius is half the diameter, so $r = 8/2 = 4$ cm. Now we have $r = 4$ and $h = 9$ to use in the formula.

Substitute $r = 4$ and $h = 9$ into $V = \pi r^2 h$: $V = \pi \cdot 4^2 \cdot 9 = \pi \cdot 16 \cdot 9 = \pi \cdot 144$. Therefore, the volume is $144\pi$ cubic centimeters, which corresponds to choice B.