SOLUTION: A right circular cylinder of height 12cm and radius 4cm is filled with water. A heavy circular cone of height 9cm and base radius 6cm is lowered, with vertex downwards and axis ver

Question 1136735: A right circular cylinder of height 12cm and radius 4cm is filled with water. A heavy circular cone of height 9cm and base radius 6cm is lowered, with vertex downwards and axis vertical, into the cylinder until the cone rests on the rim of the cylinder. Find the
1. volume of water which spills over from the cylinder, and
2. height of the water in the cylinder after the cone has been removed.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The volume of the cylinder is

The portion of the cone that is inside the cylinder is similar to the whole cone. The radii of those two cones are in the ratio 2:3; since the cones are similar, the ratio of their heights is also 2:3. That makes the height of the small cone 2/3 of 9, which is 6. Then the volume of the cone that is inside the cylinder is

ANSWER 1: The volume of water that spills from the cylinder when the cone is lowered into it is the volume of the small cone: 32pi (cm^3).

The volume of water that spilled from the cylinder, 32pi, is 1/6 of the volume of the cylinder. So when the cone is removed, the volume of water in the cylinder will be 5/6 of the original volume. Then since the cylinder has constant radius, the height of the water in the cylinder after the cone is removed is 5/6 of the full height of the cylinder.

ANSWER 2: The height of water in the cylinder after the cone is removed is (5/6)*12 = 10cm.

-----------------------------------------------------------------
Thanks to tutor @Ikleyn for noticing the errors in my original response, now fixed

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.

The solution by @greenestamps is perfect, but his last paragraph before the ANSWER 2 has typos.

I came to correct them:

The volume of water that spilled from the cylinder, 32pi, is 1/6 of the volume of the cylinder. So when the cone is removed, the volume of water in the cylinder will be 5/6 of the original volume. Then since the cylinder has constant radius, the height of the water in the cylinder after the cone is removed is 5/6 of the full height of the cylinder.

RELATED QUESTIONS
A metal solid right circular cone of base radius 4cm and height 12cm is put into a hollow (answered by mathslover)
Find the surface area of a right circular cone with radius of 5cm and height of... (answered by rfer)
Find the surface area of a right circular cylinder whose height is 12cm and the radius is (answered by jojo14344)
a right circular cone has an altitude of 18 inches and a radius of 8 inches and is 1/4... (answered by ikleyn)
a right circular cone has an altitude of 18 inches and a radius of 8 inches and is 1/4... (answered by ikleyn)
a right circular cone has an altitude of 18 inches and a radius of 8 inches and is 1/4... (answered by Boreal,ikleyn)
Find the surface area of a circular cylinder with radius of 4cm and a height of... (answered by jim_thompson5910)
A conical hole is drilled in a circular cylinder of height 12cm and base radius 5cm. The... (answered by Alan3354)
A conical hole is drilled in a circular cylinder of height 12cm and base radius 5cm . The (answered by Alan3354)