The height of a right rectangular prism is three times the width of the base. The length of the base is twice the width.

A rectangular prism is shown. The rectangular bases have side lengths of 2 and 2 w. The height of the prism is 3 w.

Which expression represents the volume of the prism in terms of w, the width of the base?

5w2 cubic units
6w2 cubic units
5w3 cubic units
6w3 cubic units

Respuesta :

Answer:6w^3

Step-by-step explanation: The volume of a right rectangular prism is the product of its dimensions:

V = LWH

= (2w)(w)(3w) = 6w³ . . . . cubic units

The expression that represents the volume of the rectangular prism in terms of w, the width of the base is 6w³ cubic units

Volume of a rectangular prism

The volume of a rectangular prism can be represented as follows:

volume = lwh

where

  • l = length
  • w = width
  • h = height

Therefore,

width = w

height = 3w

length = 2w

Therefore, the volume can be represented as follows:

volume = w × 3w × 2w

volume = w × 6w²

volume = 6w³ cubic units

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