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.

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**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

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