Question 996162
the volume of the cone is equal to 1/3 * pi * r^2 * h


r is the radius
h is the height.
d is the diameter
the radius is equal to 1/2 tghe diameter.


you have:


d = 60 cm
h = 24 cm
r = d/2 = 30 cm


v = 1/3 * pi * r^2 * h becomes v = 1/3 * pi * 30^2 * 24 which becomes v = 7200 * pi.


that part's ok.


the volume of a cylinder is equal to pi * r^2 * h


d = diameter
r = radius
h = height


you have:


d = 40
r = d/2 = 20
h = what you want to find.
v = 7200 * pi which is the volume from the cone that's poured into the cylinder.


v = pi * r^2 * h becomes 7200 * pi = pi * 20^2 * h


simplify to get 7200 * pi = 400 * pi * h


divide both sides of this equation by 400 * pi to get:


(7200 * pi) / (400 * pi) = h


solve for h to get h = 18 cm.


the height of the water in the cylindrical container is 18 cm.


v = pi * r^2 * h becomes v = pi * 20^2 * 18 becomes v = pi * 400 * 18 becomes v = pi * 7200.


you have the same volume in the tank as the volume that was in the cylinder when the height of the water in the cylinder is 18 cm.