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A spiral staircase turns 270 degrees as it rises 10 feet. The radius of the staircase is 5 feet. What is the number of feet in the length of the handrail? Express your answer as a decimal to the nearest tenth.

 Apr 20, 2021
 #1
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We  call "un -wrap"  the staircase  to  make  a  rectangle

 

The bottom  of  the  rectange =  (3/4)  * 2pi  *  5   =   7.5 pi   ft

 

The  height of  the  rectangle =  10   ft

 

The length of  the   handrail  =   the  diagonal length of the  rectangle  =

 

  sqrt [ 10^2  + ( 7.5 pi)^2  ] ≈  25.6  ft

 

 

cool cool cool

 Apr 20, 2021

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