Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to example 4 in section 3.7). if the cup is 6 inches tall and the top has a radius of 3 inches, how fast is the water level rising when the water is 4 inches deep?

The water level rising when the water is 4 inches deep is .

Step-by-step explanation:

Rate of water pouring out in the cone = R=

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

r = h/2

Volume of the cone =

h = 4 inches

The water level rising when the water is 4 inches deep is .

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584