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The approximate change in the volume of ...

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is(A) 0.06 `x^3m^3` (B) 0.6 `x^3m^3` (C) 0.09 `x^3m^3` (D) 0.9 `x^3m^3`

A

`0.06 x^(3) m^(3)`

B

`0.6x^(3) m^(3)`

C

`0.09x^(3) m^(3)`

D

`0.9x^(3) m^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Edge of cube = x
` :." volume "V= x^(3)`rArr (dV)/(dx) = 3x^(2)`
Now, change in volume `Delta V = (dV)/(dx) Dleta x = 3x^(2) * Dleta x`
`= 3x^(2) xx (3/(100x)`
` = 0.09x^(3) m^(3)` .
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