/sci/ - Science & Math

[Anonymous No.1986726]

Differential calculus, easy shit, just wanted to check in with you guys to see if i'm doingitright.

A conical tank is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

dv/dt = 10 ft^3/min, volume of a cone = (1/3)(pi)(r^3)(h). Deriving with respect to dh/dt returns 2/3(pi)(r)(dh/dt)(h).

10 = 2/3(pi)(r)(dh/dt)(h), substituting known values (r = 5, h = 8) and dividing out returns

dh/dt = 3/(8(pi)) as final answer.

[Anonymous No.1986730]

[Anonymous No.1986735]