A cone has a height of #16 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #9 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2018-04-30T02:12:19

#color(brown)("Surface Area " =802.79 " " cm^2#

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#"Given : " H = 16cm, h = 9cm, R = 7cm#

#r = (h / H) * R = (9/16) * 7 = 3.94cm#

#"Slant height of the cone " s = sqrt(H^2 + R^2)#

#s = sqr(16^2 + 7^2) = 17.46#

#"Surface Area " = piR^2 + pir^2 + pi s (R + r)#

#=> pi*7^2 + pi * 3.94^2 + pi * 17.46 * (7 + 3.94)#

#=> 153.94 + 48.77 + 600.08 = 802.79 " " cm^2#