A cone has a height of #18 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #4 cm# from the base, what would the surface area of the bottom segment be?

2 Answers
Apr 15, 2018

#:.color(purple)(=172.22cm^2# to the nearest 2 decimal places cm^2#

Explanation:

:.Pythagoras: #c^2=18^2+4^2#

#:.c=L=sqrt(18^2+4^2)#

#:. c=Lcolor(purple)(=18.439cm#

#:.18/4=tan theta=4.5=77^@28’16.2”#

:.#color(purple)(S.A.#= pir^2+pir*L#

:.S.A.#=pi*4*18.439#

:.S.A.#=231.711#

:.Total S.A.#color(purple)(=262.116cm^2#

#:.Cot 77^@28’16.2”*14=3.111cm=#radius of top part

:.Pythagoras: #c^2=14^2+3.111^2#

#:.c=L=sqrt(14^2+3.111^2)#

#:. c=Lcolor(purple)(=14.341cm# top part
:.S.A. top part#=pi*r*L#

S.A. top part#:.pi*3.111*14.341#

S.A. top part#:.=140.162#

S.A. top part#:.color(purple)(=140.162cm^2#

:.S.A. Bottom part#color(purple)(=231.711-140.162=91.549cm^2#

:.S.A. Bottom part#=91.549+30.408+50.265=172.222 cm^2#

#:.color(purple)(=172.22cm^2# to the nearest 2 decimal places # cm^2#

Apr 15, 2018

#:.color(purple)(=172.22cm^2# to the nearest 2 decimal places # cm^2#

Explanation:

:.Pythagoras: #c^2=18^2+4^2#

#:.c=L=sqrt(18^2+4^2)#

#:. c=Lcolor(purple)(=18.439cm#
#:.18/4=tan theta=4.5=77^@28’16.2”#

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

:.S.A.#=pi*4*18.439#

:.S.A.#=231.711#

:.Total S.A.#color(purple)(=231.711cm^2#

#:.Cot 77^@28’16.2”*14=3.111cm=#radius of top part

:.Pythagoras: #c^2=14^2+3.111^2#

#:.c=L=sqrt(14^2+3.111^2)#

#:. c=Lcolor(purple)(=14.341cm# top part
:.S.A. top part#=pi*r^2+pi*r*L#

S.A. top part#:.pi*3.111*14.341#

S.A. top part#:.=140.162#

S.A. top part#:.color(purple)(=140162cm^2#

:.S.A. Bottom part#color(purple)(=231.711-140.162=91.549cm^2#

#91.549+30.408+50.265=172.222#

#:.color(purple)(=172.22cm^2# to the nearest 2 decimal places # cm^2#