A 50% increase does not mean adding 50 to a number. How can you rewrite a 50% increase as a multiplication factor?

First find the new radius and new height after increasing each by 50%. Then plug those new values into the cylinder volume formula.

When you use the radius in the formula, do you square it or leave it as is? Make sure you apply that step correctly for the new radius.

In Desmos, type pi*(12)^2*15 and note the decimal output; this is the numerical value of the larger cylinder's volume.

Type each choice into Desmos (e.g., 1360*pi, 1620*pi, 2160*pi, 2400*pi) and compare their decimal values to the one you found for pi*(12)^2*15. The correct answer choice is the one whose decimal value matches.

The volume $V$ of a right circular cylinder with radius $r$ and height $h$ is

We will use this formula with the new radius and new height after the 50% increase.

A 50% increase means multiplying by $1.5$ (since $1 + 0.5 = 1.5$).

• Original radius: $8$ cm $\Rightarrow$ new radius: $8 \times 1.5 = 12$ cm
• Original height: $10$ cm $\Rightarrow$ new height: $10 \times 1.5 = 15$ cm

So the larger cylinder has radius $12$ cm and height $15$ cm.

Substitute $r = 12$ and $h = 15$ into $V = \pi r^2 h$:

Compute the square of the radius first:

so the volume becomes

Now multiply $144 \times 15$:

So the volume of the larger cylinder is

which corresponds to answer choice C) $2{,}160\pi$.