SURFACE AREAS
AND VOLUMES
and Hemisphere
A vessel is in the form of a hollow hemisphere mounted by a
hollow cylinder. The diameter of the hemisphere is 14 cm and the total
height of the vessel is 13cm. Find the inner surface area of the vessel.
13cm
The vessel is made up
of cylinder and a
hemisphere
Inner surface area of vessel =
CSA of cylinder (S1) +
CSA of hemisphere (S2)
7cm
7cm
7cm
6cm
Sol.
Diameter =
14 cm
Radius =
14
= 7 cm
2
d
2
=
7
∴
Let us find the height of the cylinder
Height of cylinder
= Height of vessel
– Height of Hemisphere
13 –
=
7
6 cm
=
?
14cm
2 π r h
2 π r2
?
✔
?
?
What is the formula to find curved surface area of hemisphere?
What is the formula to find curved surface area of cylinder?
✔
✔
We know that,
Radius =
Height
In Hemisphere,
Q.
13cm
7cm
Sol.
CSA of Cylinder (S1)
=
2 π r h
=
2 × π
× 7
× 6
=
84π cm2
CSA of Hemisphere (S2)
=
2 π r2
=
2 × π
× 7
× 7
=
98π cm2
6cm
7cm
7cm
CSA of Cylinder (S1)
CSA of Hemisphere (S2)
∴
∴
A vessel is in the form of a hollow hemisphere mounted by a
hollow cylinder. The diameter of the hemisphere is 14 cm and the total
height of the vessel is 13cm. Find the inner surface area of the vessel.
Inner surface area of vessel =
CSA of cylinder (S1) +
CSA of hemisphere (S2)
Q.
2 π r h
2 π r2
182
7
Inner surface area of the vessel is 572 cm2
26
Sol.
Inner surface area
of the vessel
=
S1 + S2
=
84π
+ 98π
=
182
× π
=
×
22
=
26
× 22
=
572 cm2
13cm
7cm
7cm
7cm
6cm
S1 = 84π
S2 = 98π
∴
A vessel is in the form of a hollow hemisphere mounted by a
hollow cylinder. The diameter of the hemisphere is 14 cm and the total
height of the vessel is 13cm. Find the inner surface area of the vessel.
Inner surface area of vessel =
CSA of cylinder (S1) +
CSA of hemisphere (S2)
Q.
2 π r h
2 π r2