SOLUTION: If a hemispherical bowl of radius 6cm contains water to a depth of x cm the volume of the water is 1/3pix^2(18-x) cm^3. Water is poured into the bowl at a rate of 3cm^3/s. Find the

Algebra ->  Test  -> Lessons -> SOLUTION: If a hemispherical bowl of radius 6cm contains water to a depth of x cm the volume of the water is 1/3pix^2(18-x) cm^3. Water is poured into the bowl at a rate of 3cm^3/s. Find the      Log On


   

Question 1048414: If a hemispherical bowl of radius 6cm contains water to a depth of x cm the volume of the water is 1/3pix^2(18-x) cm^3. Water is poured into the bowl at a rate of 3cm^3/s. Find the rate at which the water level is rising when the depth is 2cm.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If a hemispherical bowl of radius 6cm contains water to a depth of x cm, the volume of the water is
V%28x%29+=+%281%2F3%29pi%2Ax%5E2%2818-x%29cm%5E3.........you have the volume as a function of depth
Water is poured into the bowl at a rate 3cm%5E3%2Fs . Find the rate at which the water level is rising when the depth is x=2cm.

V+=+%281%2F3%29pi%2Ax%5E2+%2818-x%29
V=+6pi%2Ax%5E2+-+%281%2F3%29pi%2Ax%5E3

dV%2Fdt+=+12pi%2Ax+%28dx%2Fdt%29+-+pi%2Ax%5E2%28+dx%2Fdt%29
3+=+%28dx%2Fdt%29%2812pi%2Ax+-+pi%2Ax%5E2%29
when x+=+2
3+=+%28dx%2Fdt%29%2812%2A2%2Api-+4pi%29
3+=+%28dh%2Fdt%29%2824+pi-+4pi%29
dx%2Fdt+=+%283%2F%2820pi%29%29+%28cm%2Fs+%29...exactly
dx%2Fdt+=+0.15%2A3.14+%28cm%2Fs+%29->dx%2Fdt+=+0.471+%28cm%2Fs+%29........approximately