Ex 12.1, 2
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 13 cm. Find the inner surface area of the vessel.
Now,
Inner surface area of the vessel
= Curved surface area of hemisphere
+ Curved surface area of the cylinder
Curved Surface area of hemisphere
Diameter of hemisphere = 14 cm
Radius of hemisphere = r = 14/2 = 7 cm
Curved surface area of hemisphere = 2𝜋𝑟2
= 2 ×22/7×(7)2
= 2 × 22/7 × 7 × 7
= 2 × 22 × 7
= 308 cm2
Curved surface area of cylinder
Curved Surface area of cylinder = 2𝜋𝑟ℎ
Radius of cylinder = Radius of hemisphere = r = 7 cm
Height of cylinder = Total height – Radius of hemisphere
= 13 – 7
= 6 cm
Curved Surface area of the cylinder = 2𝜋𝑟ℎ
= 2 ×22/7 × 7 × 6
= 2 × 22 ×6
= 264 cm2
Now,
Inner surface area of the vessel
= Curved surface area of hemisphere
+ Curved surface area of the cylinder
= 308 + 264
= 572 cm2
Hence, Inner surface area of vessel is 572 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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