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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?

User Colabug
by
6.0k points

1 Answer

4 votes

Answer:


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

User Jim Holden
by
6.4k points
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