A cone has a height of #16 cm# and its base has a radius of #2 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2017-12-23T08:47:28

T S A = 55.2926 #cm^2#

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#OA = h = 16 cm, OB r = 2 cm, , AF = h_1 = 16-3 = 13 cm#

#FD = r_2 =( h_1 /h)*r = (13/ 16) * 2 = 1.625 cm#

#AC = l = sqrt(h^2 + r^2) = sqrt(16^2 + 2^2) = 16.1245 cm #

#AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(13^2 + 1.625^2) = 13.1012 cm#

#pir^2 = pi*2^2 = 12.5664 cm^2#

#pir_2^2 = pi*1.625^2 = 8.2958 cm^2#

#pirl= pi* 2 * 16.1245 = 101.3132 cm^2#

#pir_2l_1 = pi* 1.625 * 13.1012 = 66.8828 cm^2#

Total surface area = #(pir^2 + pir_1^2 + pi.r.l - pi.r_2.l_1)#

# T S A = 12.5664 + 8.2958 + 101.3132 - 66.8828 = #55.2926 #cm^2#