A cone has a height of #9 cm# and its base has a radius of #4 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 · 2018-05-27T15:26:25

#:.color(purple)(=141.36cm^2# to the nearest 2 decimal places # cm^2#

:.Pythagoras: #c^2=9^2+4^2#

#:.c=L=sqrt(9^2+4^2)#

#:. c=Lcolor(purple)(=9.849cm#

#:.9/4=tan theta=2.25=66^@02’15”#

:.#"color(purple)(S.A".##=pi*r*L#

:.S.A.#=pi*4*9.849#

:.S.A.#=123.766#

:.Total S.A.#color(purple)(=123.766cm^2#

#:.Cot 66^@02’15”*6=2.667cm=#radius of top part

:.Pythagoras: #c^2=6^2+2.667^2#

#:.c=L=sqrt(6^2+2.667^2)#

#:. c=Lcolor(purple)(=6.566cm# top part

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

S.A. top part#:.pi*2.667*6.566#

S.A. top part#:.=55.014#

S.A. top part#:.color(purple)(=55.014cm^2#

:.S.A. Bottom part#color(purple)(=123.766-55.014=68.758cm^2#

:.S.A. Bottom part#=68.758+pir^2+pir^2#

#:.68.758+22.340+50.265#

#:.color(purple)(=141.363cm^2# to the nearest 2 decimal places # cm^2#