Question

A spherical glass vessel has a cylindrical neck that is 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water the vessel can hold.

Answer 1

Diameter of spherical part = 21 cm
Radius of the spherical part = 10.5 cm

Volume of spherical part of the vessel $=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\times \frac{22}{7}\times 10.5\times 10.5\times 10.5=4851{\mathrm{cm}}^3$
Diameter of cylinder = 4 cm
Radius of cylinder = 2 cm
Height of cylinder = 7 cm

Volume of the cylindrical part of the vessel $=\pi r^{2}h=\frac{22}{7}\times 2\times 2\times 7=88{\mathrm{cm}}^3$

Total volume of the vessel$=4851+88=4939c{m}^3$