Question

1. A solid sphere of radius r is melted and casted into shape the shape of a solid cone of height r . Find the radius of base of the cone

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Answer 1

Answer:

Let the radius of cone be R .

Height of cone = r .

Whenever the shape is recast , then the volume of the figure will be conserved always .

Volume of sphere is $\frac{4}{3}\pi r^3$ .

Volume of cone is $\frac{1}{3}\pi r^2h$

Volume of cone will be equal to the volume of the sphere .

$\implies \frac{1}{3}\pi R^2r=\frac{4}{3}\pi r^3\\\\\implies R^2r=4r^3\\\\\implies R^2=4r^2\\\\\implies R=\sqrt{4r^2}\\\\\implies R=2r$

The radius of the cone will be twice the radius of sphere .

Answer 2

Question

1. A solid sphere of radius r is melted and casted into shape the shape of a solid cone of height r . Find the radius of base of the cone.

Answer

Given, radius of solid sphere = r

Height of solid cone = R

now, since the solid sphere is recasted into an solid cone.

HENCE,     Volume of cone = Volume of Cylinder

=> 1/3 ×$\pi$ ×R² × h = 4/3 × $\pi$ × r³

=> 1/3 × $\pi$ × R²  = 4/3 ×$\pi$ × r

=>  R²   =   4r²

                                   = > R  = 2r

Hence the radius of base of the cone will be 2 times the radius of solid sphere.

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