A cone has a height of #8 cm# and its base has a radius of #6 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?

1 Answer

Answer:

#282.74"cm"^2"to the nearest 2 decimal places"#enter image source here

Explanation:

#tan theta=8/6=1.333333333=53^@7'48''#

#"top radius"=cot 53^@7'48''=0.75 xx4=3.0cm #

#Lateral area= F=pi(r_1+r_2)sqrt((r_1-r_2)^2+h^2)#

#F=pi(6+3)sqrt((6-3)^2+4^2)#

#F=pi(9)sqrt((9+16)#

#F=9pisqrt25#

#F=28.27433388 xx5=141.3716694"cm"^2#

#S=F+pi(r_1^2+r_2^2)#

#S=141.3716694+pi(6^2+3^2)#

#S=141.3716694+pi(36+9)#

#S=141.3716694+pi(45)#

#S=141.3716694+141.3716694#

#S=282.7433388"cm"^2#

#S="surface area of bottom segment"#

#=282.74"cm"^2"to the nearest 2 decimal places"#