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
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.
2 answers
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
Solve any question of Surface Areas and Volumes with:-
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
Solve any question of Surface Areas and Volumes with:-