Three identical balls, each of radius 3.5 cm, are stacked inside a closed cylindrical can of radius 3.5 cm and height 21 cm, so that the can is exactly filled top to bottom by the stack. Find the volume of empty space inside the can, in cubic centimetres. (Take π = 22/7.)

Question

Accepted Answer

269.5. Can = \π r^2 h = 22/7(12.25)(21) = 808.5 cm³. One ball = 4/3\π r^3 = 4/3 × 22/7 × 42.875 = 179.67 cm³, so three balls = 539 cm³. Empty space = 808.5 − 539 = 269.5 cm³ — exactly one third of the can, a result that holds for any such stack. 539 is the balls; 808.5 is the whole can; 628.83 removes only one ball.

Three identical balls, each of radius 3.5 cm, are stacked inside a closed cylindrical can of radius 3.5 cm and height 21 cm, so that the can is exactly filled top to bottom by the stack. Find the volume of empty space inside the can, in cubic centimetres. (Take π = 22/7.)

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