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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

ConceptArea and Volume of Solids - Sphere

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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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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