Michael J. answered • 10/04/16

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Effective High School STEM Tutor & CUNY Math Peer Leader

Since we have a length, width, and height, we have a rectangular prism.

a)

The volume of a rectangular prism is the product of those dimensions.

xyh = V

Plug in the know values into this equation.

xy(1.5) = 6

xy(3/2) = 6

xy = 6(2/3)

xy = 4

y = 4 / x

**y(x) = 4 / x**

b)

We take the surface area of the prism. Keep in mind of the open top. However, the glass is only applied to the sides.

SA = 2xh + 2yh

Then plug in the value of y from the previous solution as well as h so that the total area is in terms of x.

S(x) = 2x(3/2) + 2(4/x)(3/2)

S(x) = 3x + 12/x

**S(x) = (3x**

^{2}+ 12) / x