Question
The ratio of volumes of spheres A and B is 8:27. If the
difference between their total surface area is 3080 cm² then find diameter of sphere A. (in cm)Solution
ATQ,
Volume ratio A:B = 8:27 → radii ratio = 2x : 3x Surface area of A = 4π(2x)² = 16πx² Surface area of B = 4π(3x)² = 36πx² Difference = 36πx² – 16πx² = 20πx² = 3080 Solve: 20πx² = 3080 x² = 3080 / (20 × 3.1416) ≈ 49 x = 7 Radius of A = 2x = 14 Diameter = 2 × radius = 28 cm
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