A cone has a height of #6 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #2 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2017-10-20T03:22:53

Total Surface Area = 315.5493 cm^2

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#OA = h = 6 cm, OB r = 6 cm, , AF = h_1 = 4 cm#

#FD = r_2 =( h_1 /h)*r = (4 / 6)6= 4 cm#

#AC = l = sqrt(h^2 + r^2) = sqrt(6^2 + 6^2) = 8.4853#

#AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(4^2 + 4^2) = 5.6569 cm#

#pir^2 = pi*6^2 = 113.0973cm^2#

#pir_2^2 = pi*4^2 = 50.2655 cm^2#

#pirl= pi 6 8.4853 = 159.4413 cm^2

#pir_2l_1 = pi* 4 * 5.6569 = 8.2548#

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

# T S A = 113.0973+ 50.2655 + 159.4413 - 8.2548 =**314.5493 ** cm^2**#