Question

A piece of rectangular crafting supply is being cut for a new sculpture. You want its length to be three times its height and its width to be two times its height. If you want the wood to be 162 cubic centimeters, what will its length, width, and height be? Use x for the height of the piece of crafting supply.

Answer 1

Length = 9 cm

Weight = 6 cm

Height = 3 cm

Explanation:

Given the height of rectangular piece =
`x` cm

Length = 3 times the height =
`3x`

Width = 2 times the height =
`2x`

Volume of rectangular piece = 162 cubic cm

Let us have a look at the formula for volume of a rectangular shape 3D sculpture i.e. a Cuboid.

Volume = Length
`*` Width
`*` Height

Putting all the given values:

`162=3x* 2x* x\\\Rightarrow 6x^3=162\\\Rightarrow x^3=(162)/(6)\\\Rightarrow x^3 =27\\\Rightarrow \bold{x =3 \ cm}`

Therefore, the answer is:

Length = 3
`*` 3 = 9 cm

Width = 3
`*` 2 = 6 cm

Height = 3 cm