Ex 12.2, 8
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3 . Check whether she is correct, taking the above as the inside measurements, and π= 3.14.
Now,
Volume of vessel
= Volume of sphere + Volume of cylinder
Volume of sphere
Diameter = 8.5 cm
Radius = r = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/2 = 8.5/2 = 4.25 cm
Volume of sphere = 4/3 𝜋𝑟3
= 4/3×3.14×(4.25)3
= 321.39 cm3
Volume of cylinder
Diameter = 2 cm
Radius = r = 𝐷𝑎𝑖𝑚𝑒𝑡𝑒𝑟/2 = 2/2 = 1 cm
Height of cylinder = h = 8 cm
Volume of cylinder = 𝜋𝑟2ℎ
= 3.14 × (1)2 × (8)
= 3.14 × 8
= 25.12 cm3
Now,
Volume of vessel = Volume of sphere + Volume of cylinder
= 321.39 + 25.12
= 346.51 cm3
Hence, volume obtained by child is incorrect,
correct volume is 346.51 cm3

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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