Posted by **simran** on Tuesday, December 4, 2012 at 6:35am.

A Toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere .If the radius of base of the cone is 21 cm and its volume is 2/3 of the volume of hemisphere calculate the height of cine and surface area of the toy.

- maths -
**Reiny**, Tuesday, December 4, 2012 at 8:19am
The missing part is the height of the cone, but it is 2/3 the volume of the hemisphere (semi-sphere).

volume of hemisphere = (1/2 (4/3)π (21^3) = 6174π

but the volume of the cone is 2/3 of that or 4116π

vol of cone = (1/3)π r^2 h

4116π = (1/3)π(21^2)h

12348 = 441h

h = 28

Now use your formulas for surface area of a sphere, take half of that , and use your formula for the surface area of a cone with radius 21 and height 28

Make sure NOT to include the circular base joining them when finding surface area

## Answer this Question

## Related Questions

- maths-surface area - A solid is in the form of cone mounted on a hemisphere in ...
- Math - a cone and a hemisphere share the base that is a semicirclee with radius ...
- math - Two right circular cone, one upside down in the other. The two bases are ...
- Calculus - Given a right circular cone, you put an upside-down cone inside it so...
- geometry - A cone is topped with a hemisphere. Calculate the total surface area ...
- maths --plse help me.. - A toy is in the shape of a right circular cylinder with...
- Calculus: Optimization - I have no idea how to approach this problem, if someone...
- Math 214 - How do you find the volume of a right circular cone with a hemisphere...
- MATH214 - Find the surface area of a right circular cone topped with a ...
- MATH214 - Find the surface area of a right circular cone topped with a ...