# Thread: Related Rates are SO CONFUSING ...

1. ## Related Rates are SO CONFUSING ...

The sun is shining and a spherical snowball of volume 110 ft3 is melting at a rate of 11 cubic feet per hour. As it melts, it remains spherical. At what rate is the radius changing after 4 hours?

I thought for related rates you need to take the deriviative and then plug in the values. But the derivative of the volume equation for a sphere does not have a variable for time - so them where does the 4 go? Oi. Someone help me ???

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A lighthouse is fixed 200 feet from a straight shoreline. A spotlight revolves at a rate of 10 revolutions per minute, (20 p rad/min ), shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along the shoreline 19 feet from the shoreline point closest to the lighthouse?

For this one, I am utterly confused.

2. Originally Posted by Moco
The sun is shining and a spherical snowball of volume 110 ft3 is melting at a rate of 11 cubic feet per hour. As it melts, it remains spherical. At what rate is the radius changing after 4 hours?
given ...

volume at time $t = 0$ is $110 \, ft^3$

$\frac{dV}{dt} = -11 \, ft^3/hr$

after 4 hrs , $V = 110 - 4(11) = 66 \, ft^3$

what would $r$ be at this time?

$V = \frac{4}{3} \pi r^3$

$\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}$

substitute in your given and calculated values, and solve for $\frac{dr}{dt}$

3. Thank you!