The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. find the diameter of the base of the cone.
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. find the diameter of the base of the cone.

Height of the solid right circular cone = 32 cm

Internal radius metallic spherical shell = 3 cm

External radius spherical shell = 5 cm

the volume of the spherical shell

    \[\begin{array}{*{35}{l}} =\text{ }4/3\text{ }\pi \text{ }\left( {{5}^{3}}~-\text{ }{{3}^{3}} \right)  \\ =\text{ }4/3\text{ x }22/7\text{ x }\left( 125\text{ }-\text{ }27 \right)  \\ =\text{ }4/3\text{ x }22/7\text{ x }98  \\ \end{array}\]

Volume of solid right circular cone

    \[\begin{array}{*{35}{l}} =\text{ }1/3\text{ }\pi {{r}^{2}}h  \\ =\text{ }1/3\text{ x }22/7\text{ x }{{r}^{2}}~x\text{ }32  \\ 1/3\text{ x }22/7\text{ x }{{r}^{2}}~x\text{ }32\text{ }=\text{ }4/3\text{ x }22/7\text{ x }98  \\ {{r}^{2}}~=\text{ }\left( 4\text{ x }98 \right)/\text{ }32  \\ r\text{ }=\text{ }7/2\text{ }=\text{ }3.5\text{ }cm  \\ \end{array}\]

Therefore, diameter = 2r = 7 cm