Question

Suppose a triangular prism has surface area 84 square centimeters and volume 36 cubic centimeters. The prism is dilated by scale factor k=4. Calculate the surface area and volume of the dilated prism.

Answer 1

To find the surface area of the dilated prism, multiply the surface area of the original prism by the scale factor squared. To find the volume of the dilated prism, multiply the volume of the original prism by the scale factor cubed.

Step-by-step explanation:

To find the surface area of the dilated prism, you need to multiply the surface area of the original prism by the scale factor squared. So, the surface area of the dilated prism is 84 * (4^2) = 84 * 16 = 1344 square centimeters.

To find the volume of the dilated prism, you need to multiply the volume of the original prism by the scale factor cubed. So, the volume of the dilated prism is 36 * (4^3) = 36 * 64 = 2304 cubic centimeters.