The radius of a spherical balloon is increasing at the rate of 0.4 cm divided by minute0.4 cm/minute. How fast is the volume changing when the radius is 7.47.4 cm?

Question

Mathematics

Rhys Vasquez

27 September, 17:01

The radius of a spherical balloon is increasing at the rate of 0.4 cm divided by minute0.4 cm/minute. How fast is the volume changing when the radius is 7.47.4 cm?

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Answers (1)

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Simeon Cobb · Answer 1

Dr/dt = 0.4

v = 4/3 pi r^3

dv/dr = 4 pi r^2

dv/dt = dv/dr * dr / dt = 4/0.4 pir^2 = 10 pi r^2

When radius is 7.4 volume is increasing by:-

dv/dt = 10pi7.4^2 = 1720.34 cm^3 / minute Answer