A copper sphere of radius 3 cm is melted and recast into a right circu

1.	A copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm. Find the radius of the base of the cone.
Answer» Volume of the sphere = \(\frac{4}{3}πR^3\) = \(\frac{4}{3}π{3}^3\) Volume of the cone = \(\frac{1}{3}πr^2h\) = \(\frac{1}{3}πr^2\times3\) Volume of the cone = volume of the sphere \(\frac{1}{3}πr^2\times3\)= \(\frac{4}{3}π{3}^3\) ⇒ \(\frac{1}{3}\times{r}^2\times3\) = \(\frac{4}{3}\times{3}^3\) ⇒ r²= \(\frac{{4} \times{3} \times{3}\times{3}\times{3}}{{3}\times{3}}\) ⇒ r² = 36 cm ⇒ r = 6 cm

A copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm. Find the radius of the base of the cone.

Answer»

Volume of the sphere = \(\frac{4}{3}πR^3\)

= \(\frac{4}{3}π{3}^3\)

Volume of the cone = \(\frac{1}{3}πr^2h\)

= \(\frac{1}{3}πr^2\times3\)

Volume of the cone = volume of the sphere

\(\frac{1}{3}πr^2\times3\)= \(\frac{4}{3}π{3}^3\)

⇒ \(\frac{1}{3}\times{r}^2\times3\) = \(\frac{4}{3}\times{3}^3\)

⇒ r²= \(\frac{{4} \times{3} \times{3}\times{3}\times{3}}{{3}\times{3}}\)

⇒ r² = 36 cm

⇒ r = 6 cm