Find the length of the arc, which forms an angle of #90^@# at the center of a circle whose radius is #8# #cm.#?

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Answer 1 · 2017-03-16T04:47:23

#12.6# #cm#

Consider the diagram

enter image source here

The length of an arc with radius #r# and vertex angle #theta# is

#color(brown)(theta/360*2pir#

#rarr90/360*2*22/7*8#

#rarr1/cancel4^1*2*22/7*cancel8^2#

#rarr2*22/7*2#

#rarr4*22/7#

#rarr4*3.14#

#color(green)(rArr12.56# #color(green)(cm)#

Rounded off to the nearest tenth will be #12.6# #cm#

Hope this helps! :)