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The volumes of two spheres are in the ratio 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 cm.

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Let the radii of the two spheres be r1 cm and r2 cm respectively and their respective volumes be V1 and V2. Then,

Given, r1 + r2 = 7 ⇒ \(\frac43r^2+r^2\) = 7 ⇒ \(\frac{7r_2}{3}\) = 7 ⇒ r2 = 3 cm.

∴ r1 = \(\frac43\times3\) = 4 cm
∴ Difference in the surface areas of the two spheres = \(4πr^2_2-4πr^2_1\)

\(4π(r^2_2-r^2_1)\) = 4 x \(\frac{22}{7}\times(16-9) =4\times\frac{22}{7}\times7\) cm2 = 88 cm2.

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