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 27 times the volume of the original tanks.
c. the volume of the new tanks will be 9 times the volume of the original tanks.
d. the volume of the new tanks will be 81 times the volume of the original tanks.

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume formula of a cylinder is \(V = \pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Determine the new radius and height

The new radius \(r_{new}=3r\) and the new height \(h_{new} = 3h\).

Step3: Calculate the new volume

Substitute into the volume formula: \(V_{new}=\pi(3r)^{2}(3h)\).

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Since the original volume \(V=\pi r^{2}h\), we have \(V_{new}=27V\).

Answer:

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