Question

a cylinder has a height of 5 feet and a radius of 2 ft. if a scale model of the cylinder is scaled up by a factor of 3, what is the surface area of the model? 132.65 ft² 791.68 ft² 865.28 ft² 756.20 ft²

Explanation:

Step1: Find the new radius and height

The original radius $r = 2$ ft and height $h=5$ ft. Scaled up by a factor of 3, the new radius $R = 2\times3=6$ ft and new height $H = 5\times3 = 15$ ft.

Step2: Recall the surface - area formula for a cylinder

The surface - area formula of a cylinder is $A=2\pi R^{2}+2\pi RH$.

Step3: Calculate $2\pi R^{2}$

$2\pi R^{2}=2\pi\times6^{2}=2\pi\times36 = 72\pi$.

Step4: Calculate $2\pi RH$

$2\pi RH=2\pi\times6\times15=180\pi$.

Step5: Calculate the total surface area

$A = 72\pi+180\pi=252\pi$. Using $\pi\approx3.14$, we have $A\approx252\times3.14 = 791.28$ ft².

Answer:

$791.28$ ft²