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 (ratio of corresponding linear dimensions) is \( k \), the volume scales by \( k^3 \) and the surface area scales by \( k^2 \).

Step2: Find the scale factor \( k \)

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

Step3: Find the surface area scale factor

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

Answer:

4 (corresponding to the option "4")