A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 12 cm.

Question

anonymous · Answer

Do you know an equation that represents the volume of a sphere and the diameter?

anonymous · Answer

v = 4π/3 r3
my answer is 135.71, and so is my friend's i am confused. went online to see, same answer.

anonymous · Answer

Well, the radius is half the diameter, and you want to express it in diameter, so it would be$$V = \frac{4}{3}\pi(\frac{d}{2})^3$$. Then you need to differentiate with respect to time

anonymous · Answer

first off your answer should be negative

anonymous · Answer

(Note the answer is a positive number).

anonymous · Answer

really? how is it positive if the volume is decreasing?

anonymous · Answer

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 12 cm. (Note the answer is a positive number).

anonymous · Answer

Semantics "At what rate is the volume of the snowball decreasing" I guess they mean the magnitude since they already ask for the decreasing value

anonymous · Answer

lol

anonymous · Answer

i will guess that if the diameter is decreasing at a rate of .3 cm/minute then the radius is decreasing at a rate of  0.15 cm / minute
differentiate 
$$V=\frac{4}{3}\pi r^3$$ get 
$$V'=4\pi r^2 r'$$ replace $r'$ by $0.15$ and $r$ by $6$ and see what you get