Question

A right circular cone of height 8.4cm and the radius of base is 2.1cm.it is melted and recast into a sphere . find the radius of the sphere.

Answer 1

Hey there,

Given
Radius of cone =2.1cm
Height of cone =8.4cm

Volume of cone =
1/3πr²h
= 1/3 x 22/7 x 2.1² x 8.4

=38.808cm³

Volume of cone = volume of sphere

Volume of sphere =
4/3 πr³
4/3 x 22/7 x r³ = 38.808

r³=38.808x21/88=9.261cm

r³ = 9261 / 1000 cm

r=21/10=2.1CM

Hope this helps!

Answer 2

Hello,

we know that: the right circular cone is melted and recast into a sphere, then the volume of cone will be exactly equal to the volume of sphere.
Vc= Vs;
πR²h/3= 4πr³/3;π×2.1²×8.4/3=4πr³/3;
38.808 = 4πr³/3;
3×38.808=4πr³/3;
4πr³=116.424;
r³=116.424/4π;
r³ = 9.261;
r = ∛9.261;
r = 2.1 cm

So, the radius of the sphere is 2.1 cm

bye :-)