One night, hans decides to cook a hamburger and spaghetti with meatballs. to test ideas of surface-to-volume ratios, he makes a quarter pound hamburger and a quarter pound meatball and cooks them at the same temperature. which food item will cook the fastest and why

Hamburger , High surface area

Explanation:

The higher the surface area , the higher is the heat absorption. With this logic, a sphere has a low surface-to-volume ratio while a cube or cuboid has a large surface-to-volume ratio comparatively and hence cuboid must absorb more heat.

A hamburger is more or less like a shape of cuboid while meat balls are of shape of sphere. Thus keeping all conditions constant i.e constant weight, volume and temperature of cooking,  it is the hamburger that will cook the fastest due to high surface area.