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The given figure shows a solid sphere and a closed cylindrical container, both having the same heights and same radii. The volume of air left in the cylinder is :

  1. 6πr3

  2. 32πr3\dfrac{3}{2}πr^3

  3. 23πr3\dfrac{2}{3}πr^3

  4. 4πr3

The given figure shows a solid sphere and a closed cylindrical container, both having the same heights and same radii. The volume of air left in the cylinder is : Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.

Mensuration

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Answer

From figure,

Radius of sphere = Radius of cylinder = r

Height of cylinder (h) = 2r

Volume of air left = Volume of cylinder - Volume of sphere

=πr2h43πr3=πr2.2r43πr3=2πr343πr3=6πr34πr33=2πr33=23πr3.= πr^2h - \dfrac{4}{3}πr^3 \\[1em] = πr^2.2r - \dfrac{4}{3}πr^3 \\[1em] = 2πr^3 - \dfrac{4}{3}πr^3 \\[1em] = \dfrac{6πr^3 - 4πr^3}{3} \\[1em] = \dfrac{2πr^3}{3} \\[1em] = \dfrac{2}{3}πr^3.

Hence, Option 3 is the correct option.

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