JEE MATHEMATICS MCQ: RATE MEASURE

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A balloon is pumped at the rate of

\mathrm{cm}^3 /

minute. The rate of increase of its surface area when the radius is b

\mathrm{cm}

, is -

View answer and explanation

Correct option: C

(2 \mathrm{a} / \mathrm{b}) \mathrm{cm}^2 / \mathrm{min}

Option C (

(2a / b) \text{{ cm}}^2 / \text{{min}}

) is correct because differentiating the volume and surface area formulas with respect to time and then substituting r=b leads to this rate of increase.

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The surface area of a sphere when its volume is increasing at the same rate as its radius, is A particle is moving in a straight line has velocity and displacement equation as

v = 4\sqrt {1 + s}

where

v

velocity in m/s and

s

m

. The initial velocity of the particle is The diagonal of a square is changing at the rate of 0.5 cm

{s^{ - 1}}

. Then, the rate of change of area , when the area is 400

c{m^2}

is equal to A spherical balloon is filled with

4500 \pi

cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of

72 \pi

cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is: A solid box is formed by placing a cylinder, having equal height and radius on top of a cube such that, the circular base of cylinder is the inscribed circle for square top of the cube. If the radius of cylinder is changing at the rate

\frac{1}{2 \pi+16}

\mathrm{cm} / \mathrm{sec}

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