Question

If the side of a cube is increased by x%, then find the percentage increment of its volume.

• A. [(1+x/100)³-1] 100 %
• B. [(1+x/100)³-1] %
• C. [(1+2x/100)³-1]
• D. None of these

Answer 1

The correct option is A

[(1+x/100)³-1] 100 %

Let the side of a cube be a units

Volume of cube = $sid{e}^3$ = $a^3$ cu. units.

Side of the a square increases by x %

Now, side of a cube = $a+(a\times \frac{x}{100})$ = $a+\left(\frac{ax}{100}\right)$

Volume of cube = ${(a+\frac{ax}{100})}^3$ cu. units.

Increase in the volume = (new volume – old volume)

= $(a+(a+\frac{ax}{100}){)}^3-a^3)$ = $a^3({[1+\frac{x}{100}]}^3–1)$

So, percentage increase = $\frac{Increaseinthevolume}{oldvolume}\times 100\%$

= $\frac{\left[a^3({[1+\frac{x}{100}]}^3-1)\right]}{a^3}$ $\times$ $100\%$

= $[{(1+\frac{x}{100})}^3-1]$ $100\%$