A cone has a height of #14 cm# and its base has a radius of #8 cm#. If the cone is horizontally cut into two segments #5 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Dec 24, 2017

T S A = 521.9289 #cm^2#

Explanation:

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#OA = h = 14 cm, OB r = 8 cm, , AF = h_1 = 14-5 = 9 cm#

#FD = r_2 =( h_1 /h)*r = (9/ 14) * 8 = 5.1429 cm#

#AC = l = sqrt(h^2 + r^2) = sqrt(14^2 + 8^2) = 16.1245 cm #

#AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(9^2 + 5.1429^2) = 10.3658 cm#

#pir^2 = pi*8^2 = 201.0619 cm^2#

#pir_2^2 = pi*5.1429^2 = 83.0933 cm^2#

#pirl= pi* 8 * 16.1245 = 405.2529 cm^2

#pir_2l_1 = pi* 5.1429 * 10.3658 = 167.4792 cm^2

Total surface area = #(pir^2 + pir_2^2 + pi.r.l - pi.r_2.l_1)#

T S A = 201.0619 + 83.0933 + 405.2529 - 167.4792 = 521.9289 #cm^2#