Question

A solid metallic cone of radius 2 cm and height 8 cm melted into a sphere, find the radius of sphere.

Answer 1

radius of solid sphere formed should be 2cm

Answer 2

The radius of sphere is 2 cm

Step-by-step explanation:

Radius of cone = 2 cm

Height of Cone = 8 cm

Volume of cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 2^2 \times 8$

Let teh radius of sphere be r

Volume of sphere = $\frac{4}{3} \pi r^3= \frac{4}{3} \times \frac{22}{7} \times r^3$

Since A solid metallic cone of radius 2 cm and height 8 cm melted into a sphere So, volume remains same

$\frac{1}{3} \times \frac{22}{7} \times (2)^2 \times 8 = \frac{4}{3} \times \frac{22}{7} \times r^3\\(2)^2 \times 8 =4r^3\\\sqrt[3]{\frac{2^2 \times 8}{4}}=r\\2=r$

Hence The radius of sphere is 2 cm

#Learn more :

12 solid spheres of same size are made by melting a solid metallic cone of base radius 1 cm and height of 48 cm find the radius of each sphere

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