Question

a cone is 8.4cm high and the radius of its base is 2.1cm. it is melted and recast into a sphere . find the radius is the sphere

Answer 1

Hey

Case of cone :-

• Height = 8.4 cm

• Radius = 2.1 cm

So , volume :-

= 1 / 3 * pie * height * ( radius ) ²

= 1 / 3 * pie * 8.4 * ( 2.1 ) ²

= 1 / 3 * pie * 8.4 * 2.1 * 2.1 cm³

Now ,

Let the radius of sphere be x cm .

So volume of sphere :-

= 4 / 3 * pie * ( radius ) ³

= 4 / 3 * pie * ( x ) ³ cm³

Now , in recasting any figure into any other figure , the volume remains same .

So ,

Volume of sphere = volume of cone

=> 4 / 3 * pie * ( x ) ³ = 1 / 3 * pie * 8.4 * ( 2.1)²

=> 4 * ( x ) ³ = 8.4 * 2.1 * 2.1

=> ( x ) ³ = 2.1 * 2.1 * 2.1

=> ( x ) ³ = ( 2.1 ) ³

=> x = 2.1

So radius of sphere = 2.1 cm

thanks :)

Answer 2

the radius of the sphere is 4.52 cm
Hope this will help you