A cone has a height of #11 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #8 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2018-04-14T17:51:12

#:.color(purple)(=430.78cm^2# to the nearest 2 decimal places # cm^2#

:.Pythagoras: #c^2=11^2+7^2#

#:.c=L=sqrt(11^2+7^2)#

#:. c=Lcolor(purple)(=13.038cm#

#:.11/7=tan theta=1.571428571=57^@31’43.7”#

:.#color(purple)(S.A.#=pirL#

:.S.A.#=pi*7*13.038#

:.S.A.#=286.721#

:.Total S.A.#color(purple)(=286.721cm^2#

#:.Cot 57^@31’43.7”*3=1.909cm=#radius of top part

:.Pythagoras: #c^2=3^2+1.909^2#

#:.c=L=sqrt(3^2+1.909^2)#

#:. c=Lcolor(purple)(=3.556cm# top part

:.S.A. top part#=pi*r*L#

S.A. top part#:.pi*1.909*3.556#

S.A. top part#:.color(purple)(=21.326cm^2#

:.S.A. Bottom part#color(purple)(=286.721-21.326=26.540cm^2#

.S.A. Bottom part#=26.540+11.449+153.938=430.782 cm^2#

#:.color(purple)(=430.78cm^2# to the nearest 2 decimal places # cm^2#