Question

Question
A cylinder has a surface area of 42 π
cm2 . If it were dilated using a scale factor of 1/2
, what is the surface area of the new cylinder?(1 point)
Responses

21π cm2
21π cm2

13.5π cm2
13.5π cm2

84π cm2
84π cm2

10.5π cm2
10.5π cm2
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Answer 1

To find the surface area of the new cylinder after dilation with a scale factor of 1/2, we can use the property that the surface area of a three-dimensional object scales with the square of the scale factor.

Given that the original surface area is \( 42\pi \, \text{cm}^2 \), we can find the new surface area as follows:

1. Calculate the square of the scale factor:
\[
\left( \frac{1}{2} \right)^2 = \frac{1}{4}
\]

2. Multiply the original surface area by this factor:
\[
\text{New Surface Area} = \text{Original Surface Area} \times \frac{1}{4}
\]
\[
\text{New Surface Area} = 42\pi \times \frac{1}{4} = \frac{42\pi}{4} = 10.5\pi\, \text{cm}^2
\]

Thus, the surface area of the new cylinder after dilation is \( 10.5\pi \, \text{cm}^2 \).

The correct response is:
10.5π cm².