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

23π cm2
23 pi cm squared

368π cm2
368 pi cm squared

1,472π cm2
1 comma 472 pi cm squared

5,888π cm2

Answer 1

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

1. **Original dimensions**:
- Height (h) = 15 cm
- Radius (r) = 8 cm

2. **New dimensions after dilation**:
- New height = 4 * 15 cm = 60 cm
- New radius = 4 * 8 cm = 32 cm

3. **Surface area formula for a cylinder**:
\[
SA = 2\pi rh + 2\pi r^2
\]

4. **Calculating the new surface area**:
Substitute the new height and radius into the formula:
\[
SA = 2\pi (32)(60) + 2\pi (32^2)
\]

- Calculate \( 2\pi (32)(60) \):
\[
2\pi (32)(60) = 3840\pi \, \text{cm}^2
\]

- Calculate \( 2\pi (32^2) \):
\[
32^2 = 1024 \implies 2\pi (1024) = 2048\pi \, \text{cm}^2
\]

- Now add them together:
\[
SA = 3840\pi + 2048\pi = 5888\pi \, \text{cm}^2
\]

Therefore, the new surface area of the dilated cylinder is **5,888π cm²**.