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KEAM 2010 Math Paper

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Question : 39 of 120

Marks: +1, -0

An edge of a variable cube is increasing at the rate of

10\text{ cm/s}

. How fast the volume of the cube will increase when the edge is

5\text{ cm}

long?

$750\text{ cm}^{3}\text{/s}$
$75\text{ cm}^{3}\text{/s}$
$300\text{ cm}^{3}\text{/s}$
$150\text{ cm}^{3}\text{/s}$
$25\text{ cm}^{3}\text{/s}$

Solution:

Let a be the edge of cube.

Then,

\frac{da}{dt}=10\text{ cm/s}

(Given).....(i)

∵ Volume of cube is

V=a^{3}\text{ cm}^{3}

\Rightarrow\;\frac{dV}{dt}=3a^{2}\;\frac{da}{dt}\;\text{cm}^{3}\text{/s}

=3\times5^{2}\times10\text{ cm}^{3}\text{/s}

[Using Eq. (i)]

=750\text{ cm}^{3}\text{/s}

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