Question

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

Answer 1

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

Volume of cone =
$\frac{1}{3} \pi {r}^{2} h$
$= \frac{1}{3} \times \frac{22}{7} \times {2.1}^{2} \times 8.4$
=38.808cm³

Volume of cone = volume of sphere

Volume of sphere =
$\frac{4}{3} \pi {r}^{3}$
$\frac{4}{3} \times \frac{22}{7} \times {r}^{3} = 38.808$
r³=38.808x21/88=9.261cm

${r}^{3} = \frac{9261}{1000} cm$
r=21/10=2.1CM

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 :-)