Question
A right circular cylinder is partially filled with
water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls areSolution
Let the radii of the spherical balls be r cm and r/2 cm. The radius of the cylinder R = 18/2 = 9 cm. According to the question (4/3)π [r3 + (r / 2)3] = π R 2 h (4/3) [r3 + (r3) / 8] = 9 × 9 × 4 9r3/8 = 9 x 9 x 3 R3 = 9 × 3 × 8 r = ∛ [3 × 3 × 3 × 2 × 2 × 2] r = 3 × 2 r = 6cm r / 2 = 3cm So, the radii of the cylinder are 3 cm and 6 cm.
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