Ex 12.1, 4
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
The hemisphere can occupy
whole of the side of cube.
Hence,
Greatest diameter of hemisphere = Side of cube = 7 cm
Here, base of hemisphere falls on cube, so that Area should not from part of solid.
Thus,
Surface area of solid = Area of cube
+ Curved surface area of hemisphere
– Base area of hemisphere
Area of cube
Here, a = Side = 7 cm
Area of cube = 6a2
= 6 (7)2
= 6 × (7× 7)
= 6 × 49
= 294 cm2
Curved surface area of hemisphere
Diameter of hemisphere = 7 cm
∴ Radius = r = (Diameter )/2 = 𝟕/𝟐 cm
Now,
Curved Surface area of hemisphere = 2𝜋𝑟2
= 2 ×22/7×(7/2)^2
= 2 ×22/7×7/2×7/2
= 77 cm2
Base area of hemisphere
Base of hemisphere is a circle with
Radius = radius of hemisphere = r = 7/2 cm
Base area of hemisphere = πr2
= 22/7×(7/2)^2
= 22/7×7/2×7/2
= 𝟕𝟕/𝟐 cm2
Now,
Surface area of solid = Area of cube
+ Curved surface area of hemisphere
– Base area of hemisphere
= 294 + 77 – 77/2
= 294 + 77 – 38.5
= 371 – 38.5
= 332.5 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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