Question

a new company uses cylindrical gas tanks to deliver propane gas. as their orders increase, they switch to new gas tanks with triple the height and triple the radius of the original tanks. what will be the effect of the scaled dimensions on the volume of the tanks?
a. the volume of the new tanks will be 3 times the volume of the original tanks.
b. the volume of the new tanks will be 9 times the volume of the original tanks.
c. the volume of the new tanks will be 81 times the volume of the original tanks.
d. the volume of the new tanks will be 27 times the volume of the original tanks.

Explanation:

Step1: State original cylinder volume

The volume of a cylinder is given by $V_{original} = \pi r^2 h$, where $r$ = original radius, $h$ = original height.

Step2: Define new dimensions

New radius $r_{new} = 3r$, new height $h_{new} = 3h$.

Step3: Calculate new volume

Substitute new dimensions into the volume formula:

$$\begin{align*} V_{new} &= \pi (3r)^2 (3h)\\ &= \pi \cdot 9r^2 \cdot 3h\\ &= 27\pi r^2 h \end{align*}$$

Step4: Compare volumes

Since $V_{original} = \pi r^2 h$, $V_{new} = 27V_{original}$.

Answer:

D. The volume of the new tanks will be 27 times the volume of the original tanks.