Question

1. A 12 cm by 25 cm by 36 cm box of cereal is lying on the floor on one of its 25 cm by 36 cm faces. An ant, located at one of the bottom corners of the box, must crawl along the outside of the box to reach the opposite bottom corner. What is the length of the shortest path? (* note: The ant can crawl on any of the 5 exposed faces) (*note: The ant cannot crawl on the bottom, which is flush with the ground). It can crawl on any edge or face of the box

Hint: Pythagorean theorem.

Answer 1

43.83cm

Explanation:

There are only two faces that are 25cm by 36cm, the top and the bottom face. Since, the ant, cannot move across the bottom face, we are left with the top face which is a rectangle. The shortest distance is through the diagonal.

Drawing a diagonal, you have two right-angled triangles. Bringing any out, we would need to know the length of the diagonal which is the hypotenuse of the right angle triangle. Using Pythagoras theorem:

(Hypotenuse)^2 = (opposite)^2 + (adjacent)^2

H^2 = 25^2 + 36^2

H^2 = 625 + 1296

H^2 = 1921

H = sqrt (1921)

H = 43.83 cm (to 2 d.p.)

H which represents the hypotenuse, that is the diagonal is the shortest distance. Hence, the shortest distance is 43.83cm.