A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21cm. Find the quantity of water it can hold. [Use π = 22/7]
Length of cylindrical neck = l = 7 cm
Diameter of cylindrical neck = 4 cm
Radius of cylindrical neck = r = Diameter ÷ 2 = 4/2 cm = 2 cm
Volume of cylindrical neck = πr2l
= 22/7 × 2 × 2 × 7 cm3
= 88 cm3
Diameter of spherical part = 21 cm
Radius of spherical part = r’ = Diameter ÷ 2 = 21/2 cm = 10.5 cm
Volume of spherical part = 4/3 πr’3
= 4/3 × 22/7 × 10.5 × 10.5 × 10.5 cm3
= 4851 cm3
Quantity of water spherical glass vessel with cylindrical neck can hold = Volume of spherical part + Volume of cylindrical neck
Quantity of water spherical glass vessel with cylindrical neck can hold = 4851 cm3 + 88 cm3 = 4939 cm3
Quantity of water spherical glass vessel with cylindrical neck can hold is 4939 cm3.