Question

A hollow sphere of internal and external radius 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

Answer 1

Internal radius of a hollow sphere (r) = 2 cm and external radius (R) = 4 cm
$\therefore$ Volume of the metal used
$=\frac{4}{3}\pi (R^3-r^3)=\frac{4}{3}\pi [4^3-2^3]=\frac{4}{3}\pi [64-8]c{m}^3=\frac{224}{3}\pi c{m}^2$
Now, volume of cone $=\frac{224}{3}\pi c{m}^2$ and radius = 4 cm
$\therefore \left(h\right)=\frac{volume\times 3}{\pi r^2}=\frac{224\pi \times 3}{3\times \pi \times 4\times 4}cm=14cm\therefore Slantheight=\sqrt{r^2+h^2}=\sqrt{(4{)}^2+(14{)}^2}=\sqrt{16+196}=\sqrt{212}cm=14.56cm$