MODELING WITH MATHEMATICS You are building a birdhouse in the shape of a rectangular prism that has a volume of 128 cubic inches. The dimensions of the birdhouse in terms of its width are shown.

Question

a. Write a polynomial that represents the volume of the birdhouse.

 in.³

b. What are the dimensions of the birdhouse?

length:   in., width:   in., height:   in.

Answer 1

V =LWH = 128

without more information there is no unique solution

but given a generally sized birdhouse, maybe 8 x 4 x 4

4 inch height, 4 inch width, 8 inch length. W=H, L=2W or W+4

Then V(W) = WW(2W) = 2W^3

or V= W(W)(W+4) = W^3 +4W^2 if you want a polynomial

V(4) = 4^3 + 4(4^2 = 64+ 64 = 128