• # question_answer A hollow sphere of external and internal radius 6 cm and 4 cm respectively is melted into a cone of base diameter 8 cm. find the height of the cone. A)  4.75 cm                       B)  9.5 cm       C)  19 cm             D)  38 cm

(d): The volume in both the cases would be the same. Let the height of the cone = h, its radius = 4 cm Hollow sphere:- Then, external radius = 6 cm Internal radius $=4\,\,cm$ $\Rightarrow$   $\frac{4\pi \left( {{6}^{3}}-{{4}^{3}} \right)}{3}=\frac{\pi {{.4}^{2}}.h}{4}$ $\Rightarrow$   $h=\frac{{{6}^{3}}-{{4}^{3}}}{4}$ $\Rightarrow$   $h=\frac{216-64}{4}=38\,cm$