Question

1. there are many square prisms with volume 165 in³. let w represent the side length of the square base and h represent the height in inches. then the formula for the volume v, in cubic inches, of these prisms is v = w²h, and the equation for the surface area s, in square inches, is s = 2w² + 4wh. write an equation for s as a function of w when the volume of the prism is 165 in³. explain or show your work.

Explanation:

Step1: Express \( h \) in terms of \( w \)

Given \( V = w^{2}h=165 \), so \( h=\frac{165}{w^{2}} \).

Step2: Substitute \( h \) into the surface - area formula

The surface - area formula is \( S = 2w^{2}+4wh \).
Substitute \( h=\frac{165}{w^{2}} \) into \( S = 2w^{2}+4wh \):

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Answer:

\( S(w)=2w^{2}+\frac{660}{w}\)