Question

pyramid a has a surface area of 256 square inches. pyramid a is dilated by a scale factor of 0.5 to create pyramid b. what is the surface area, in square inches, of pyramid b?

Explanation:

Step1: Recall the scale factor for surface area

When a 3D figure is dilated by a scale factor \( k \), the surface area of the new figure is \( k^2 \) times the surface area of the original figure. Here, the scale factor \( k = 0.5 \).

Step2: Calculate the surface area of Pyramid B

First, find \( k^2 \): \( k^2=(0.5)^2 = 0.25 \). Then, multiply this by the surface area of Pyramid A (256 square inches). So, the surface area of Pyramid B is \( 256\times0.25 \).
\( 256\times0.25 = 64 \)

Answer:

64