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Question 83
Three solid metallic spheres whose radii are 1 cm, X cm and 8 cm, are melted and recast into a single solid sphere of diameter 18 cm. The surface area (in $$cm^2$$) of the sphere with radius x cm is:
Solution
Volume of solid sphere = $$\frac{4}{3} \pi r^3$$
Radius of single solid sphere = 18//2 = 9 cm
Volume of single solid sphere = Volume of three solid metallic spheres
$$\frac{4}{3} \pi (9)^3$$ = $$\frac{4}{3} \pi[1^3 + x^3 + 8^3]$$
$$729 = 512 + 1 + x^3$$
$$x^3 = 216$$
x = 6 cm
Surface area = $$4\pi r^2 = 4\pi 6^2 = 144 \pi$$
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