An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 3 cm.

6.913 cubic-meters/second.

Step-by-step explanation:

Volume of pyramid is.

and

we essentially need to compute derivative at h = 3.

but firs we need to write s in terms of h only, to do that we use the fact that ration of side to height of a pyramid is always constant, which means.

solving for s and substituting in Volume function gives.

and taking derivative with respect to time gives.

but we have been given that piece of information so.

at h = 3 in above we have finally.

. + λrh() e 1 1 2 4 4 4 4 4 3 4 4 4 4 4 + th−1(− s(x)2 dx ω + λrh−1() e 2 1 2 4 4

step-by-step explanation:

1/2*qr*rs

step-by-step explanation: