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A balloon, which always remains spherical on inflation, is bei

Question

A balloon, which always remains spherical on inflation, is being inflated by pumping in $900$ cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15 c m$ .

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A balloon, which always remains spherical on inflation, is being inflated by pumping in

900

cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is

15 c m

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

The volume of a sphere

(V)

with radius

(r)

is given by,

V = \frac{4}{3} π r^{3}

∴

Rate of change of volume

(V)

with respect to time

(t)

is given by,

\frac{d V}{d t} = \frac{d V}{d r} \cdot \frac{d r}{d t} = 4 π r^{2} \cdot \frac{d r}{d t}

It is given that

\frac{d V}{d t} = 900 c m^{3} / s

∴ 900 = 4 π r^{2} \cdot \frac{d r}{d t}

\Rightarrow \frac{d r}{d t} = \frac{900}{4 π r ^{2}} = \frac{225}{π r ^{2}}

Therefore, when radius

= 15

cm,

\frac{d r}{d t} = \frac{225}{π ( 15 ) ^{2}} = \frac{1}{π}

cm/s

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Question Text	A balloon, which always remains spherical on inflation, is being inflated by pumping in $900$ cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15 c m$ .
Answer Type	Text solution:1
Upvotes	150