Question

if rate of increase of volume of is 80 when radius is 2 then rate at which the radius is increasing is given by
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Answer 1

If rate of increase of volum of is180 when radius is 2 then rate at which the radius is increasing is given by.

Answer 2

The rate of increase in radius is 2 units

Given:

The rate of increase of volume is 80 when the radius is 2 units

To find:

The rate at which the radius is increasing is given by

Solution:

Complete question:

For a sphere, if the rate of increase of volume is 80π when the radius is 2 the rate at which the radius is increasing is given by  

The formula for the volume of the sphere is given by

Volume of sphere, v = 4/3 π r³  

Differentiate v with respect to t

=> dv/dt = 4/3 π (3) (r²) dr/dt

=> dv/dt = 4π (r²) dr/dt

From the data,

The rate of increase of volume is 80π and the radius is 2 units

=> 80π = 4π (r²) dr/dt  

=> 20 = (2)² [ dr/dt ]

=> [ dr/dt ] = 20/4

=> [ dr/dt ] = 5

Therefore,

The rate of increase in radius is 2 units

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