Question

There are many square prisms with volume 125in³. 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 125 in³.

Answer 1

To write the equation for surface area S as a function of the side length w when the volume is 125 in³, substitute the given volume into the formula for volume and rearrange to solve for h. Then, substitute the value of h into the formula for surface area and we get s= = 2w² + 500/w..

Step-by-step explanation:

To write an equation for the surface area S as a function of the side length w when the volume of the square prism is 125 in³, we can use the given formula for the surface area: S = 2w² + 4wh.

Since the volume of the prism is given as 125 in³, we can substitute V = 125 into the volume formula V = w²h. Rearranging this equation gives us h = V/w²

= 125/w².

Substituting this value of h into the equation for the surface area, we get: S = 2w² + 4w(125/w²)

= 2w² + 500/w.