Mata's box for her art materials is a cuboid 35cm by 28cm by 15cm. She has a thin paintbrush which is 48cm long.

will this paintbrush fit into Mata's box
show your calculations to support your answer

Question

Mata's box for her art materials is a cuboid 35cm by 28cm by 15cm. She has a thin paintbrush which is 48cm long.

will this paintbrush fit into Mata's box
show your calculations to support your answer

jim_thompson5910 · Answer

To find the longest possible length in this box, we need to find the length of the diagonal that stretches from one corner to the opposite corner.



So to do that, we apply the pythagorean theorem in 3 dimensions



d = sqrt(L^2+W^2+H^2)


d = sqrt(35^2+28^2+15^2)


d = 47.2652091923859



Since this distance is less than 48, this means that the paint brush will NOT fit.