Question

The radius of an air bubble is increasing at the rate of $\frac{1}{2}$ $\text {cm} /\text s.$. At what rate is the volume of the bubble increasing when the radius is 1 $\text {cm}$?

Answer 1

volume of the bubble increasing is increasing at rate of 2 × pie cm^3/s when radius = 1cm

Step-by-step explanation:

dr/dt = 1/2

r = radius

air bubble is spherical

volume v= (4/3) × pie × r^3

dv/dt = 4 × pie × r^2 (dr/dt)

r = 1 cm

dr/dt = 1/2

dv/dt = 4 × pie × 1^2 (1/2)

= 2 × pie cm^3/s

volume of the bubble increasing is increasing at rate of 2 × pie cm^3/s when radius = 1cm

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Answer 2

Answer:

volume of the bubble increasing is increasing at rate of 2 × pie cm^3/s when radius = 1cm

Step-by-step explanation:

dr/dt = 1/2

r = radius

air bubble is spherical

volume v= (4/3) × pie × r^3

dv/dt = 4 × pie × r^2 (dr/dt)

r = 1 cm

dr/dt = 1/2

dv/dt = 4 × pie × 1^2 (1/2)

= 2 × pie cm^3/s

volume of the bubble increasing is increasing at rate of 2 × pie cm^3/s when radius = 1cm