• # question_answer A spherical metal ball of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by n%. Then n =? A)  900   B)  800          C)  600                             D)  200

(a): Let radius of a smaller sphere be ?r cm?. $\frac{4}{3}\times \pi \times {{(10)}^{3}}=1000\times \frac{4}{3}\times \pi \times {{(r)}^{3}}$ $r=1\,\,cm$ Surface area of the larger sphere $=4\pi {{(10)}^{2}}$                                                 $=400\pi$ Total surface area of 1000 smaller spheres $=1000\times 4\pi {{(1)}^{2}}=4000\pi$ Increase in the surface area $=4000\pi -400\pi$                                         $=3600\pi$ Hence, surface area of the metal is increased by 900%. Therefore n = 900.