Question

A block of wood is a cube whose side is x in. long. You cut off a 1-inch thick piece from the entire right side. Then you cut off a 3-inch thick piece from the entire top of the remaining shape. The volume of the remaining block is 2,002 in3. What are the dimensions of the original block of wood?

Answer 1

Answer: 14 in x 14 in x 14 in

Explanation:

Given: A block of wood is a cube whose side is x in. long.

Then according to the question, the dimensions of the remaining block be x, x-1,x-3

Then volume of the remaining block is given by:-

`x(x-1)(x-3)=2002\\\Rightarrow\ x^3-4x^2+3x-2002=0`

By rational root theorem, the possible zeroes are=
`(p)/(q)`

Now, here p=2002 and q=1

Then the possible zeroes are factors of 2002,

Now, the factors of 2002=
`1,2,7,11,13,14,143,77,22,91,....`

When we check the above values in the equation, only x=14 satisfy the equation.

Such that
`14(14-1)(14-3)=2002`

hence, the dimensions of the original block of wood= 14 in x 14 in x 14 in