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Question 5
Sam wants to build a toy box in the shape of a rectangular prism that will
hold 36 cubic feet. If the height needs to be 1 foot less than the width and
the length is twice the width, find the height of the toy box.

Respuesta :

Considering the volume of the given rectangular prism, the height is of 5.03 feet.

What is the volume of a rectangular prism?

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, we have that:

  • h = w - 1 -> w = h + 1.
  • l = 2w = 2(h + 1) = 2h + 2.

The volume is of 365 cubic feet, hence:

lwh = 365

(2h + 2)(h + 1)h = 365

(2h² + 4h + 2)h - 365 = 0

2h³ + 4h² + 2h - 365 = 0.

Using a cubic equation calculator, the height is of h = 5.03 feet.

More can be learned about the volume of a rectangular prism at https://brainly.com/question/17223528

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