A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 8 in?

Shania Houston

Shania Houston

Answered question

2023-03-12

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 8 in?

Answer & Explanation

Jazlene Martin

Jazlene Martin

Beginner2023-03-13Added 4 answers

The formula for volume of a sphere is V = 4 3 r 3 π
Differentiating with respect to t , time.
d V d t = 4 r 2 ( d r d t )
The rate of change of the snowball is given by d V d t . We know d r d t = - 4 . We want to find the rate of change when r = 8 . Thus,
d V d t = 4 ( 8 ) 2 ( - 4 )
d V d t = 4 ( 64 ) ( - 4 )
d V d t = - 1024
Consequently, the snowball's volume is shrinking at a rate of - 1024 in 3 sec

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