Geometry and TrigonometryVery hardHeight of water from a melted sphere
Geometry and Trigonometry practice question
A solid sphere of ice with radius 3 centimetres melts completely into an empty cylindrical glass with inside radius 3 centimetres. Assuming the water has the same volume as the ice, how high, in centimetres, does the water stand in the glass?
Answer: 4
The sphere's volume is (4/3)π(27) = 36π; dividing by the glass's base area 9π gives a height of 4.
Common wrong answers
- If you answered 3
- 3 is the radius.
- If you answered 12
- 12 forgets to divide by 3 in the sphere's volume.
- If you answered 36
- 36 is the volume's coefficient of π.
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