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Program for SSC CGL

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Central Government Service

Program for SSC CGL

Self Learning

₹10800 ₹6000 +
Taxes

Join Now Syllabus

Self Learning

Available

(Click here to know About SELF LEARNING)

MOCK TESTS

(Click here to attempt Free Mock Test)

Concepts Learning Progress

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Current Affair, Maths, English, History, Democratic Politics, Geography, Economics, Verbal Reasoning, Non Verbal Reasoning, General Awareness, Critical Reasoning, Verbal Ability, Vedic Maths, General Knowledge

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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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Volume of Hemisphere

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Taxes