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Maths / Surface Area and Volume / Volume of Hemisphere
(A Brief Glimpse of ABHYAS Content - Have aLook !!!!)

# Volume of Hemisphere

Volume of Hemisphere: The volume V of a hemisphere of radius r is given by  $V=\frac{2}{3}{\pi}r^{3}\;cubic \;units$

Illustration: Find the volume of a hemisphere of radius 3.5cm.

Solution: We know that the volume V of hemisphere of radius r is given by

$\dpi{100} \large \\V=\frac{2}{3}\times{\frac{22}{7}}\times{3.5}\times{3.5}\times{3.5} = \frac{11\times{49}}{3\times{2}}=89.83\;cm^{3}$

Illustration: A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

Solution:  We have, Radius of the hemispherical bowl = 18cm

Volume of the hemispherical bowl $=\frac{2}{3}{\pi}(18)^{3}\;cm^{3}$

Radius of a cylindrical bottle = 3 cm

Height of a cylindrical bottle = 6 cm

Volume of a cylindrical bottle $=(\pi \times 3^{2}\times 6)\;cm^{3}$ $=(\pi \times 9\times 6)\;cm^{3}$

Suppose x bottles are required to empty the bowl.

Volume of x cylindrical bottles $=(x\times \pi \times 9\times 6)\;cm^{3}$

Clearly, Volume of liquid in x bottles = Volume of bowl

$x\times \pi \times 9\times 6=\frac{2\pi }{3}\times (18)^{3}$

$x=\frac{2\pi \times (18)^{3} }{3\times \pi \times 9\times 6}$

$x=72$

Hence, 72 bottles are required to empty the bowl.

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