Question

You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units. You need to cut a slice off the top of the block to decrease the height by 2 units. Th e new block will have a volume of 480 cubic units. a. What are the dimensions of the new block?

Answer 1

`Depth = x= 4 units`

`length = 5x= 5(4)= 20 \ units`

`height = 2x-2= 2(4)-2= 6 \ units`

Explanation:

You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units.

height is decreased by 2 units , so height becomes 2x-2

Volume of a block is length times width time height

`volume = x \cdot 5x \cdot (2x-2)`

`480 = 10x^3-10x^2`

divide whole equation by 10

`48= x^3-x^2`

Subtract 48 from both sides

`x^3-x^2-48=0`

`\left(x-4\right)\left(x^2+3x+12\right)=0`

`x-4=0`, x=4

`Depth = x= 4 units`

`length = 5x= 5(4)= 20 \ units`

`height = 2x-2= 2(4)-2= 6 \ units`