june 2007 math b question.....need help!!!

[noreenchishti]

Q. Deenise is designing a storage box in the shape of a cube. Each side of the box has a length of 10 inches. SHE needs more room and decides to construst a larger box in the shape of a cube with a volume of 2,000 cubic inches. BY how many inches to the NEAREST TENTH, should she INCREASE the lenght of each side of the origional box?

my question is how do u start this problem.........please help!!! me out.....thnx

 

[chrisr]

hi Noreenchisti,

The original box can contain 1000 unit cubes (cubes of sides 1 inch).
This is because 10 of these unit cubes will line up in all 3 directions (up-down, left-right, front-back).

\(\displaystyle 10(10)10=10^3=1000\)

You are trying to find out the length x of a side.

\(\displaystyle x(x)x=x^3=2000\)

Therefore, x is the "cube root" of 2000.

\(\displaystyle 2000^{\frac{1}{3}}=x\)

When you discover x from this calculation, subtract 10 from it and round the answer to one decimal place.