Question

question 11 (multiple choice worth 1 points)
(scale factor and dilation mc)
a cylinder has a diameter of 10 mm and a height of 16 mm. if the cylinder is dilated with a scale factor of ( k = 3 ), what is the new surface area?
( 1,890pimathrm{mm}^2 )
( 4,680pimathrm{mm}^2 )
( 210pimathrm{mm}^2 )
( 630pimathrm{mm}^2 )

Explanation:

Step1: Calculate the original radius and surface area formula

The original diameter \(d = 10\) mm, so the original radius \(r=\frac{d}{2}=5\) mm. The height \(h = 16\) mm. The surface area formula of a cylinder is \(S=2\pi r(r + h)\).

Step2: Apply the scale - factor

When a figure is dilated with a scale factor \(k\), the new radius \(r_{new}=kr\) and the new height \(h_{new}=kh\). Here \(k = 3\), so \(r_{new}=3\times5 = 15\) mm and \(h_{new}=3\times16=48\) mm.

Step3: Calculate the new surface area

Substitute \(r_{new}=15\) and \(h_{new}=48\) into the surface area formula \(S=2\pi r(r + h)\).

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Answer:

\(1,890\pi\space mm^{2}\)