Question

In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find 

(i) The minimum total length of the escalator, 

(ii) The heights at which the escalator changes its direction, 

(iii) The slopes of the escalator at the turning points.

Answer 1

(i) the minimum total length of the escalator. Shape of the hall in the shopping mall is cuboid. When you open out the cuboid, the not of the cuboid will be as shown in the following diagram.

The path of the escalator is from OA to AB to BC to CD

The minimum length = 3280 units

(ii) The height at which the escalator changes its direction.

(iii) Slope of the escalator at the turning points

Since ∆OAE = ∆ABB’ = ∆BCC’ = ∆CAD 

Slope at the points B, C will be 9/40