Math Questions and Answers

Start Your Free Trial

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 10 cm. (Note the answer is a positive number).

Expert Answers info

Eric Bizzell eNotes educator | Certified Educator

briefcaseTeacher (K-12)


calendarEducator since 2011

write3,185 answers

starTop subjects are Math, Science, and Business

We are given the rate of decrease of the diameter `(dd)/(dt)=.1"cm"/"min" ` . We are asked to find the rate of the decrease of the volume when the diameter is 10cm:

The formula for the volume of a sphere is `V=4/3pir^3 ` .

The derivative is ` (dV)/(dt)=4pir^2(dr)/(dt) `

If the diameter is 10cm, the radius is 5cm. Also, if `(dd)/(dt)=.1 ` then `(dr)/(dt)=.05 `

Then substituting the given values:

`(dV)/(dt)=4pi(5)^2(.05)~~15.71 `

(The entire section contains 2 answers and 240 words.)

Unlock This Answer Now


check Approved by eNotes Editorial

labrat256 eNotes educator | Certified Educator

calendarEducator since 2012

write32 answers

starTop subjects are Math, Science, and History


steamgirl | Student

You can also use the equation:

V = (1/6)pi d^3

dV/dt = (1/2)pi d^2 dd/dt

Since dd/dt = .1 cm/min, and d = 10 cm, we only have to plug in and find that the answer is 15.7 cm^3/min.