Rate measure
posted by Abhi .
A balloon in the form of a right cone surmiunted by a hemispere,having a diameter equal to height of the cone,is being inflated.how fast is its volume changing w.r.t its total height 'h' when h

I assume that h is the height of the cone from the floor to the base of the hemisphere. Thus the diameter of the cone at the floor is 2 h and the height of the cone if it went to the tip would be 2 h
volume of cone of base diameter 2 h and height 2 h:
(1/3)(2h)(pi/4)(4 h^2)= (2/3)pi h^3
volume of cut off tip of cone:
(1/3)(h)(pi/4)h^2 = (1/12) pi h^3
so
volume of cone base = (7/12)pi h^3
now
volume of hemisphere = (1/2)(4/3)pi(h/2)^3 = pi h^3/12
so
total balloon volume = (2/3) pi h^3
dV/dh = 2 pi h^2
dV/dt = dV/dh * dh/dt
so
dV/dt = 2 pi h^2 dh/dt
Respond to this Question
Similar Questions

AP Calculus..again
A balloon is composed of a right circular cone joined at its base to a hemisphere. The diameter of the base is equal to the height of the cone. If the balloon is inflated, at what rate is the volume, V, changing with respect to the … 
Math
Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing … 
calculus
Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile … 
Calculus
Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile … 
calculus
Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing … 
calculus
Gravel is being dumped from a conveyor belt at a rate of cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile … 
Calculus
Grain is being dropped into a silo from a tall conveyor belt forming a right circular cone with diameter at the base equal to the height. The grain is being added at the rate of 10 cubic inches per second. How fast is the height changing … 
Calculus
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing … 
Calculus
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing … 
Related Rates
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing …