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Standard XII

Mathematics

Average Rate of Change

An edge of a ...

Question

An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast the volume of the cube will increase when the edge is 5 cm long

750

{c m}^{3} / s e c

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{c m}^{3} / s e c

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300

{c m}^{3} / s e c

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150

{c m}^{3} / s e c

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Solution

The correct option is A 750 ${c m}^{3} / s e c$
If is the length of each side of the cube and $V$ is the volume, then
$\begin{matrix} \frac{d s}{d t} = 10 V = \frac{s^{3} d v}{d t} = \frac{3 \times s^{3} d s}{d t} A t s = 5 c m, \frac{d v}{d t} = \frac{3 \times 5^{2} \times 10 c m^{3}}{s} = 750 c m^{3} / s \end{matrix}$

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An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast the volume of the cube will increase when the edge is 5 cm long

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An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast the volume of the cube will increase when the edge is 5 cm long

The correct option is A 750 cm3/secIf is the length of each side of the cube and Vis the volume, thendsdt=10V=s3dvdt=3×s3dsdtAts=5cm,dvdt=3×52×10cm3s=750cm3/s

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