If V -4-3- r 3- at what rate in cubic units is V increasing when r -10 and dr - dt -0-01 -A- 4 -B- -C- 4 -3D- 40 -

The correct option is A 4 π We have, V=4/3π r^3 ⇒dv/dt=4 π r^2dr/dt ⇒dv/dt=4 π× 100 × 0.01 [ ∵ r=10 and dr/dt=0.01 ] ⇒dv/dt=r π Hence, V is increasing at t ...

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Byju's Answer

Standard XII

Mathematics

Instantaneous Rate of Change as Slope of Tangent

If V =4/3π r ...

Question

If $V = \frac{4}{3} π r^{3}$ ,at what rate in cubic units is V increasing when r = 10 and $\frac{d r}{d t} = 0.01$ ?

$π$

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$4 π$

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$40 π$

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$4 \frac{π}{3}$

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Solution

The correct option is B
$4 π$

We have,
$V = \frac{4}{3} π r^{3} \Rightarrow \frac{d v}{d t} = 4 π r^{2} \frac{d r}{d t} \Rightarrow \frac{d v}{d t} = 4 π \times 100 \times 0.01 [∵ r = 10 a n d \frac{d r}{d t} = 0.01] \Rightarrow \frac{d v}{d t} = r π$
Hence, V is increasing at the rate of $4 π$ cubic units per unit of time.
Hence (b) is the correct answer.

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Similar questions

If $V = \frac{4}{3} π r^{3}$ ,at what rate in cubic units is V increasing when r = 10 and $\frac{d r}{d t} = 0.01$ ?

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If V=43πr3,at what rate in cubic units is V increasing when r = 10 and drdt=0.01 ?

The correct option is B 4π We have, V=43πr3⇒dvdt=4πr2drdt⇒dvdt=4π×100×0.01[∵r=10 anddrdt=0.01]⇒dvdt=rπ Hence, V is increasing at the rate of 4π cubic units per unit of time. Hence (b) is the correct answer.

If $V = \frac{4}{3} π r^{3}$ ,at what rate in cubic units is V increasing when r = 10 and $\frac{d r}{d t} = 0.01$ ?