To find the new surface area of the cylinder after applying a dilation with a scale factor of 4, we can follow these steps:
-
Determine the dimensions of the dilated cylinder:
- Original height (h) = 15 cm
- Original radius (r) = 8 cm
- After dilation (scale factor = 4):
- New height = 4 * 15 cm = 60 cm
- New radius = 4 * 8 cm = 32 cm
-
Use the formula for the surface area of a cylinder: \[ SA = 2\pi rh + 2\pi r^2 \] Replace \( r \) and \( h \) with the new values:
- \( r = 32 \) cm
- \( h = 60 \) cm
-
Calculate the surface area: \[ SA = 2\pi(32)(60) + 2\pi(32)^2 \]
- Calculating the first term: \[ 2\pi(32)(60) = 3840\pi \]
- Calculating the second term: \[ 2\pi(32)^2 = 2\pi(1024) = 2048\pi \]
- Adding the two terms together: \[ SA = 3840\pi + 2048\pi = 5888\pi \]
Thus, the new surface area of the dilated cylinder is 5,888π cm².
So the correct response is: 5,888π cm².