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Foundation program for Bank

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Banking And Insurance

Foundation program for Bank

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Maths / Surface Area and Volume / Volume of Hemisphere
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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

large V=frac{2}{3}times{frac{22}{7}}times{3.5}times{3.5}times{3.5} = frac{11times{49}}{3times{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 9times 6);cm^{3}

Suppose x bottles are required to empty the bowl.

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

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

xtimes pi times 9times 6=frac{2pi }{3}times (18)^{3}

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

x=72

Hence, 72 bottles are required to empty the bowl.


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