Ex 11.4, 2 Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?
It looks like Volume of Cylinder B is bigger
Let’s find volume and surface area of both cylinder
Volume of both cylinders
Height = 14 cm
Radius = 7/2
Volume = πr2h
= 22/7 × 7/2 × 7/2 × 14
= 11 × 1 × 7 × 7
= 539 cm3
Height = 7 cm
Radius = 14/2 = 7
Volume = πr2h
= 22/7 × 7 × 7 × 7
= 22 × 1 × 7 × 7
= 1078 cm3
Surface Area of both cylinders
Height = 14 cm
Radius = 7/2
Surface Area
= Total surface area of cylinder
= 2πr(h + r)
= 2 × 22/7 × 7/2 (14 + 7/2)
= 2 × 22/7 × 7/2 × ((14 × 2 + 7)/2)
= 22 × 35/2 = 11 × 35 = 385 cm2
Height = 7 cm
Radius = 14/2 = 7
Surface Area
= Total surface area of cylinder
= 2πr(h + r)
= 2 × 22/7 × 7 (7 + 7)
= 2 × 22/7 × 7 × 14
= 2 × 22 × 14 = 616 cm2
Hence,
Volume of Cylinder B is bigger,
and
Surface Area of Cylinder B is bigger

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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