A Florida orange grower ships orange juice in rectangular plastic containers that have square ends and are one and a half times as long as they are wide. (See the figure.)

Question

The figure is a rectangle with an x on the left side, middle, and 1.5x on the right.

(a) Find a function V that models the volume of a container of width x.

V(x) =

(b) Use the model to find the volume of a container of width 12 in.

(c) Graph the function V. Use the graph to find the width of the plastic container that has a volume of 293 in³. (Round your answer to one decimal place.)



(d) Use the graph from part (c) to find the widths for which the container has volume greater than 1,327 in³. Express your answer in interval notation.

[9.6, ∞)(−∞, 9.6]    (9.6, 1,327)[0, 1,327)[0, 9.6]

Answer 1

L=3/2 x

V=Lx^2 = (3/2)x^3

if x = 12

V = (3/2)12^3 = 2592

If V = 293 = (3/2) x^3

x^3 = 586/3 = 195 1/3

IF V = 1327 = (3/2)x^3

x^3 = (2/3)(1327) = 884 2/3

x = cube root of 884 2/3 = 9.6

x> 9.6 for Volume to be greater than 1327

x is in the interval (9.6, infinity)