IMC 2010 Q17
17. Last year Gill's cylindrical 21st birthday cake wasn't big enough to feed all her friends. This year she will double the radius and triple the height. What will be the ratio of the volume of this year's birthday cake to the volume of last year's cake?
- A 12:1
- B 7:1
- C 6:1
- D 4:1
- E 3:1
Intermediate Mathematical Challenge 2010, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 12:1
The volume of a cylinder of radius \(r\) and height \(h\) is \(\pi r^2 h\). Replacing \(r\) by \(2r\) and \(h\) by \(3h\) multiplies this volume by 12.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.