Question

A spherical glass vessel has a cylindrical neck $7cm$ long and $4cm$ in diameter. The diameter of the spherical part is $21cm$. Find the quantity of water it can hold. [Use $\pi =22/7.$]

Answer 1

A spherical vessel has a cylindrical neck which is $9cm$ long

diameter$=4cm$ (then radius $=2cm$)

diameter of the spherical part $=21cm$

also given, to find the quantity of water that it can hold

as we know that

volume of spherical vessel $=\frac{4}{3}\times \pi \times r^3$ cubic units for radius

and for diameter., volume of spherical vessel $=\frac{1}{6}\times \pi \times d^3$ cubic units

$=\frac{1}{6}\times \frac{22}{7}\times 21\times 21\times 21$

$=33\times 7\times 21$

Volume of shperical vessle $=4851{cm}^3$

as we know that

volume of cylinder neck $=\pi \times r^2\times h$cubic units

$V=\frac{22}{7}\times 2\times 2\times 7=88{cm}^3$

$\therefore$ Total volume of vessel $=$ volume of spherical vessel $+$ voluem of its cylinderical neck

$V=4851+88$

$=4939{cm}^3$

Total volume of vessel $=4939{cm}^3$

$\because$ $1L=1000mL$

$\therefore$ the amount of water the vessel can hold is $\frac{4939}{1000}=4.939L$