Question

Use the image to answer the question.

A cylinder has a height of 15 centimeters and a radius of 8 centimeters.

If the cylinder were dilated using a scale factor of 4, what would be the new surface area? The formula for the surface area of a cylinder is SA=2πrh+2πr2 .

(1 point)
Responses

1,472π cm2
1 comma 472 pi cm squared

23π cm2
23 pi cm squared

5,888π cm2
5,888 pi cm squared

368π cm2
368 pi cm squared

Answer 1

To find the new surface area of a dilated cylinder, we first need to determine the new dimensions after applying a scale factor of 4.

Original dimensions of the cylinder:
- Height (h) = 15 cm
- Radius (r) = 8 cm

After dilation with a scale factor of 4:
- New height (h') = 4 * 15 cm = 60 cm
- New radius (r') = 4 * 8 cm = 32 cm

Next, we can use the surface area formula for a cylinder, which is:

\[
SA = 2\pi rh + 2\pi r^2
\]

Now we can substitute the new dimensions into this formula.

Calculating the new surface area:

1. Calculate \(2\pi r'h'\):
\[
2\pi (32)(60) = 2\pi (1920) = 3840\pi
\]

2. Calculate \(2\pi r'^2\):
\[
2\pi (32^2) = 2\pi (1024) = 2048\pi
\]

Now, combine both parts to find the total surface area:
\[
SA' = 3840\pi + 2048\pi = 5888\pi
\]

Therefore, the new surface area of the dilated cylinder is \(5,888\pi \, \text{cm}^2\).

The correct response is:
**5,888π cm²**