Ex 13.2, 8

Transcript

Ex 13.2, 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. 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 = 12.12 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