Is there more cake or less cake?

Puzzle 4 Sweet cakes.pdf

Download PDF • 94KB

Answer

The third cake weigh more than the other two combined.

Explanation

The point of this puzzle is not to find the answer but to find the method.

We have this formula: Mass= Density x Volume

Because Volume of cylinder = Height x (π x Radius²)

=> Mass = Density x Height x (π x Radius²)

Since they have similar Densities and Heights (and π), only their radii matter.

Call the radii of the circles a, b, c with a < b < c

Thus, we have to determine if a² + b² is > or < c²

seem familiar? it's the Pythagorean theorem.

Method 1:

Cut each of the cake into 4 quadrants.

Take 3 quadrants, one from each cake, and use their radii to try to form a right triangle. Use a and b for the right-angle sides, and c for the hypontenuse. Use another quadrants (from any cake) as a triangle ruler.

• If c is longer than the hypontenus => a² + b² < c² => the third cake weigh more

• If c is shorter than the hypontenus => a² + b² > c² => the third cake weigh less

Method 2: by my friend h00p

Similar idea. This time, cut the third cake's quadrant into a righ triangle of side a and b. Then, compare that triangle's hypotenuse to c.

• If c is longer than the hypontenus => a² + b² < c² => the third cake weigh more

• If c is shorter than the hypontenus => a² + b² > c² => the third cake weigh less

Free talk

Happy birthday to me 🥳🎂