Question

A cylinder has a surface area of 54 cm?. If it were dilated using a scale factor of ½, what is the surface area of the new cylinder? (1 point)
• 13.57 cm2
О 6.75т cm2
• 277 cm2
108cm2

Answer 1

To find the surface area of the new cylinder after a dilation by a scale factor of \( \frac{1}{2} \), we need to consider how scaling affects surface area.

When a three-dimensional object is dilated by a scale factor \( k \), the surface area of the object is scaled by \( k^2 \). In this case, the scale factor is \( \frac{1}{2} \), so:

\[
k^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}
\]

Now, we will multiply the original surface area of the cylinder, which is \( 54 \, \text{cm}^2 \), by \( \frac{1}{4} \):

\[
\text{New surface area} = \text{Original surface area} \times k^2 = 54 \times \frac{1}{4} = 13.5 \, \text{cm}^2
\]

Since \( 13.5 \, \text{cm}^2 \) is not one of the given options, I will confirm whether any options match closely enough considering rounding or other potential factors.

The closest value to \( 13.5 \, \text{cm}^2 \) from the provided choices would be:

- 13.57 cm²

Thus, the surface area of the new cylinder after the dilation would be approximately:

**13.57 cm²**.