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. Show your work.
35 in
16 un
12 in






(2 points)
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

Let the tank dimensions be 35 in by 16 in (base) and height 12 in.

1) Diagonal of the bottom:
d = sqrt(35^2 + 16^2) = sqrt(1225 + 256) = sqrt(1481) ≈ 38.4838 ≈ 38.5 in (to the nearest tenth).

2) Spider's thread (space diagonal from top-back-right to bottom-front-left):
L = sqrt(d^2 + height^2) = sqrt(1481 + 12^2) = sqrt(1481 + 144) = sqrt(1625) ≈ 40.3113 ≈ 40.3 in (to the nearest tenth).

Answers: bottom diagonal = 38.5 inches; thread length ≈ 40.3 inches.