Exam 1 Review Name: 4. On a sunny winter day in Illinois, a spherical snowball h

Question

Exam 1 Review Name: 4. On a sunny winter day in Illinois, a spherical snowball has a radius of 10 cm and as it melts, the radius decreases at a rate of 0.4 cm/minute. Recall that the volume of a sphere is determined by V = 5 (a) What is the volume of the snowball 5.3 minutes after it begins melting? (b) Write a formula that expresses the radius of the snowball (in cm) in terms of the number of minutes that it has been melting. Define a function g that expresses the volume of the snowball (in cm') as a function of the amount of time (in minutes) since the snowball began melting? (c)

Explanation / Answer

r = 10 cm in the beginning
dr/dt = -0.4 cm/min

V = 4/3 * pi * r^3

At 5.3 min,
r = 10 - 0.4*5.3
r = 7.88

So, V = 4/3 * pi * 7.88^3

V = 2049.59 cm^3 ----> ANS

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b)
At the beginning , r = 10
And decreases at 0.4 cm/min, which means slope = -0.4

r = -0.4t + 10 ----> ANS

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c)
V = 4/3 * pi * r^3

So, v is :

V = 4/3 * pi * (10 - 0.4t)^3 -----> ANS

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