Please provide steps A spherical snowball Is melting in such a manner that its r

Question

Please provide steps A spherical snowball Is melting in such a manner that its radius is changing at a constant rate, decreasing from 30 cm to 15 cm in 30 minutes. At what rate, in cm^3 per minute, is the volume of the snowball changing at the instant the radius is 9 cm? -162 pi| 1215pi| -324pi| -152 pi| 81pi| A 15-foot ladder is leaning against a vertical wall. It the bottom ot the ladder is being pulled away from the wall at the rate of A feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second. at the instant the bottom of the ladder is 12 feet from the wall?

Explanation / Answer

volume of the sphere v=(4/3)pi r3

given radius changing at constant rate from 30cm to 15cm in 30min =>dr/dt =(15-30)/30=-0.5cm/min

v=(4/3)pi r3

differentiate with respect to t

dv/dt =(4/3)pi 3r2 dr/dt

dv/dt =4pi r2 dr/dt

at the instant r =9cm

dv/dt =4pi 92 *(-0.5)

dv/dt =-162pi

volume changing at -162pi cm3/min

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