Multiple choice

A hollow sphere of outer curved surface area of (324\pi) cm(^{2}) is made from (684\pi) cm(^{3}) of metal. Find the thickness of the hollow sphere.

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let outer radius = R, inner radius = r, thickness = R - r. Outer curved surface = 4πR² = 324π, so R² = 81, R = 9 cm. Volume of metal = (4/3)π(R³ - r³) = 684π. Substituting R = 9: (4/3)(729 - r³) = 684, so 729 - r³ = 513, giving r³ = 216, thus r = 6 cm. Thickness = R - r = 9 - 6 = 3 cm.

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