precalculus 12 grade

Question

Water is poured into a container in the shape of a right circular cone with radius 4 inches and height 16 inches. Express the volume the V of the water in the cone as a function of the height h of the water V= 1/3 pir^2h V(h)=

Answer 1

The radius can be viewed as a function of the height. The radius of the top of the water will be proportional to the maximum radius of the cone to the maximun height of the cone: 4 inches to 16 inches. So the radius is always 1/4 of the height of the water.

(r²h)π/3 / = ((h/4)²)hπ/3 = πr³/48

V(h) = πr³/48.