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Two Solid Spheres of Radii 2 Cm and 4 Cm Are Melted and Recast into a Cone of Height 8 Cm. Find the Radius of the Cone So Formed. - ICSE Class 10 - Mathematics

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Question

Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.

Solution

Radius of small sphere = r = 2 cm

Radius of big sphere = R = 4 cm

Volume of small sphere = `4/3 pir^3 = (4pi)/3 xx (2)^3 = (32pi)/3 cm^3`

Volume of big sphere = `4/3 piR^3 = (4pi)/3 xx (4)^3 = (256pi)/3 cm^3`

Volume of both the spheres = `(32pi)/3 + (256pi)/3 = (288pi) /3cm^3`

we need to find `R_1.h` = 8 cm (Given)

Volume of the cone = `1/3 piR_1^2 xx (8)`

Volume of the cone = Volume of both the sphere

`=> 1/3 piR_1^2 xx (8) = (288pi)/3`

`=> R_1^2 xx (8) = 288`

`=> R_1^2 = 288/8 => R_1^2 = 36`

`=> R_1 = 6 cm`

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 7.1 | 3.00 marks
Solution Two Solid Spheres of Radii 2 Cm and 4 Cm Are Melted and Recast into a Cone of Height 8 Cm. Find the Radius of the Cone So Formed. Concept: Area and Volume of Solids - Sphere.
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