The Spiral Staircase Warmup 32 A cylindrical tower is 20 met

The Spiral Staircase Warmup 3.2 A cylindrical tower is 20 meters tall and has a radius of 13 meters. A spiral staircase winds its way around the tower making two complete revolutions before arriving at the top. How long is the staircase?

Solution

Radius R = 13 meters

Total height = 20 meters

H = Rise of helix in one revolution

N = Number of turns

Calculating the length associated with one turn within the helix.

Using following formula:

L = (H^2 + C^2)^(0.5)

Here C is the circumference of the circle and is equal to :

C = 2 x 3.1416 x R

= 81.68 meters

Here the staircase rises by 10 meters after each turn (H=102) then the length associated with one turn around the staircase is:

L = (10^2 + 81.68 ^2)^(0.5) = 82.3 meters.

And the total helical length (T). To do this use the formula:

T = NL

The staircase has 2 turns , so

T = 2 * 82 = 66 meters