Question

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.

Answer 1

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 2

Volume of cone =
3
2
​
Volume of hemisphere

3
1
​
πr
2
h=
3
2
​
(
3
2
​
πr
3
) ; r =Common radius h = Cone height

h=
3
4
​
r=
3
4
​
(21)=28cm

Slant height, l=
r
2
+h
2

​
=
21
2
+28
2

​
=35cm

Total surface area = CSA
cone
​
+CSA
hemisphere
​



=πrl+2πr
2
=πr(l+2r)=5082cm
2


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