Question

Suppose a spider was able to create one thread that would extend from the top-right back corner of its tank to the bottom-left front corner. Approximately how long would that thread need to be for the tank below? The path of the spider's thread is shown with a red dotted line. Round your answer to the nearest tenth of an inch. The rectangular prism has a height of 16 in., a length of 35 in., and a width of 12 in.
The diagonal of the bottom of the tank is _____ inches. To the nearest tenth of an inch, the length of the spider's thread is _____ inches.

Answer 1

Diagonal of the bottom: sqrt(35^2 + 12^2) = sqrt(1225 + 144) = sqrt(1369) = 37 in.

Length of the thread (space diagonal): sqrt(35^2 + 12^2 + 16^2) = sqrt(1225 + 144 + 256) = sqrt(1625) ≈ 40.3 in.

So: bottom diagonal = 37 in; thread ≈ 40.3 in.