We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

A spiral staircase turns 270 degrees as it rises 10 feet. The radius of the staircase is 3 feet. What is the number of feet in the length of the handrail? Express your answer as a decimal to the nearest tenth.

Lightning Feb 3, 2019

#1**+1 **

The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle

The bottom side of the rectangle is just the arc length of a circle of a radius of 3 ft turned through 270°= (3/4) of a whole revolution....in other words.....(3/4) (2pi) (3) = (9/2)pi ft = 4.5 pi ft

The side of the rectangle will be rise of the staircase = 10ft

And the diagonal of the rectangle will be the length of the handrail

We can use the Pythagorean Theorem to solve this

handrail length = √ [ (4.5 pi)^2 + 10^2 ] ≈ 17.3 ft

CPhill Feb 3, 2019