Question

A cone is 8.4 cm high and 2.1 radius and it is melted and recast into a square find the radius of the sphere

Answer 1

***A cone is 8.4 cm high and 2.1 radius and it is melted and recast into a SPHERE. Find the radius of the sphere


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¶ Volume of cone = $\frac{1}{3}Πr^{2}h$

¶ Volume of sphere = $\frac{4}{3}Πr^{3}$


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SOLUTION:


Given,
Height of the cone = 8.4 cm
Radius of Cone base = 2.1 cm

Volume of cone = $\frac{1}{3}Π(2.1)^{2}×8.4$


Let Radius of sphere be r cm

Since a sphere is made out of a cone,
So their volumes are equal

•°• Volume of Cone = Volume of Sphere

=> $\frac{4}{3}Πr^{3} = \frac{1}{3}Π(2.1)^{2}×8.4$

=> $r^{3} = \frac{(2.1)^{2} × 8.4 × 3}{4×3}$

=> $r^{3} = (2.1)^{2} × 2.1$

=> $r^{3} = (2.1)^{3}$

=> [tex] r = 2.1 cm

•°• Radius of sphere = 2.1 cm


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Hope it helps