A cone has a height of #14 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #6 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Oct 22, 2017

# T S A = 436.2322 cm^2#

Explanation:

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#OA = h = 14 cm, OB r = 7 cm, , AF = h_1 = 8 cm#

#FD = r_2 =( h_1 /h)*r = (8 / 14) * 7 = 4 cm#

#AC = l = sqrt(h^2 + r^2) = sqrt(14^2 + 7^2) = 15.6525#

#AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(8^2 + 4^2) = 8.9443 cm#

#pir^2 = pi*7^2 = 154 cm^2#

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

#pirl= pi* 7 * 15.6525 = 344.355cm^2

#pir_2l_1 = pi* 4 * 8.9443 = 112.3973 cm^2

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

# T S A = 154 + 50.2655 + 344.355 - 112.3973 = 436.2232 cm^2**#