Question

the volume of a triangular prism is increased by a factor of 8. by what factor is the surface area of the figure increased? 2 4 16 24

Explanation:

Step1: Recall Volume and Surface Area Scaling

For similar solids, if the scale factor of linear dimensions is \( k \), the volume scales by \( k^3 \) and surface area scales by \( k^2 \).

Step2: Find Scale Factor for Volume

Given volume is increased by a factor of 8. Let the scale factor be \( k \), so \( k^3 = 8 \). Solving for \( k \), we take the cube root: \( k=\sqrt[3]{8}=2 \).

Step3: Find Scale Factor for Surface Area

Since surface area scales by \( k^2 \), substitute \( k = 2 \): \( k^2=2^2 = 4 \).

Answer:

4