mathschallenge.net

Problem

A 52 kg piece of solid hardword measuring 3" by 6"6" and 3" thick is made into a door by cutting out two rectangular panels measuring 9" by 2"6" and replacing them with glass.

If the door and glass weigh 45 kg together, what is the weight of the glass?

Solution

Volume of solid wood = 3 13/2 × 1/4 = 39/8 feet³.

Assuming uniform density, 39/8 feet³ weighs 52 kg, so 1 foot³ weighs 52/(39/8)= 32/3 kg.

Volume of one panel = 3/4 5/2 1/4 = 15/32 feet³, so volume of two panels = 15/16 feet³.

Therefore, wood removed weighs, 15/16 × 32/3 = 10 kg.

The door without the glass will be, 52 10 = 42 kg.

Hence the glass must weigh, 45 42 = 3 kg.

What if the thickness of the door was 6"?