A conical vessel of radius 6 cm and height 8 cm is filled to the brim with water. A solid ball of radius 2.1 cm is gently lowered in until it is fully under water. How much water is left in the vessel, in cubic centimetres, correct to two decimals? (Take π = 22/7.)

Question

Accepted Answer

262.91. Cone = 1/3\π r^2 h = 1/3 × 22/7 × 36 × 8 = 301.71 cm³. The ball spills its own volume: 4/3\π (2.1)^3 = 38.81 cm³. Water left = 301.71 − 38.81 = 262.91 cm³ (the ball now occupies that space). 340.52 adds the ball instead of subtracting it; 282.31 removes only 2/3\π r^3 ; 301.71 forgets the ball entirely.

A conical vessel of radius 6 cm and height 8 cm is filled to the brim with water. A solid ball of radius 2.1 cm is gently lowered in until it is fully under water. How much water is left in the vessel, in cubic centimetres, correct to two decimals? (Take π = 22/7.)

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