A) 900
B) 800
C) 600
D) 200
Correct Answer: A
Solution :
(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.
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