Question

a cylinder has a radius of 4.5 feet and a height of 12 feet. if the cylinder is dilated with a scale factor of ( k = 1.5 ), what is the new surface area?
1,187.5 ft²
1,049.7 ft²
699.8 ft²
466.5 ft²

Explanation:

Step1: Calculate the new radius and height

The new radius \(r'=4.5\times1.5 = 6.75\) feet.
The new height \(h'=12\times1.5=18\) feet.

Step2: Use the surface - area formula for a cylinder

The surface - area formula of a cylinder is \(S = 2\pi r(r + h)\).
Substitute \(r = 6.75\) and \(h = 18\) into the formula:

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Take \(\pi\approx3.14\), then \(S=13.5\times3.14\times24.75\)

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Answer:

\(1,049.7\space ft^{2}\)