Question

Outer and inner diameters of hemispherical bowl made by silver sheet are 8 cm and 4 cm respectively at its opening. The bowl is melted and a solid cone of diameter of base 8 cm is made. What is the height of the cone? ​

Answer 1

$\textbf{Given:}$

$\text{Outer and inner diameters of hemispherical bowl are 8 cm and 4 cm}$

$\text{Diameter of the base of the cone is 8 cm}$

$\textbf{To find:}$

$\text{Height of the cone}$

$\textbf{Solution:}$

$\text{Outer radius of the bowl,}\;R=4\,cm$

$\text{Inner radius of the bowl,}\;r=2\,cm$

$\text{Radius of the base of the cone formed,}\;r_1=4,cm$

$\text{When the bowl is melted,}$

$\textbf{Volume of the hemipherical bowl}=\textbf{Volume of cone}$

$\dfrac{2}{3}\pi(R^3-r^3)=\dfrac{1}{3}{\pi}{r_1}^2\,h$

$\dfrac{2}{3}\pi(4^3-2^3)=\dfrac{1}{3}{\pi}4^2\,h$

$2(64-8)=16\,h$

$2(56)=16\,h$

$56=8\,h$

$h=\dfrac{56}{8}$

$\implies\,h=7\,cm$

$\textbf{Answer:}$

$\textbf{Height of the cone is 7 cm}$