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An edge of a variable cube is increasing at the rate of 5 cm/s

Question

An edge of a variable cube is increasing at the rate of $5 c m / s$ . How fast is the volume of the cube increasing when the edge is $10 c m$ long?

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Scarlett Discussed

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

5 c m / s

. How fast is the volume of the cube increasing when the edge is

10 c m

long?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Let

x

be the length of a side and

V

be the volume of the cube.
Then,

V = x^{3}

\frac{d V}{d t} = 3 x^{2} \cdot \frac{d x}{d t},

(By chain rule)
It is given that,

\frac{d x}{d t} = 3 c m / s

∴ \frac{d V}{d t} = 3 x^{2} (3) = 9 x^{2}

Thus, when

x = 10 c m

∴ \frac{d V}{d t} = 9 (10)^{2} = 900 c m^{3} / s

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Question Text	An edge of a variable cube is increasing at the rate of $5 c m / s$ . How fast is the volume of the cube increasing when the edge is $10 c m$ long?
Answer Type	Text solution:1
Upvotes	150