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 $cm^2$

A cone has a height of 9 cm9 cm and its base has a radius of 4 cm4 cm. If the cone is horizontally cut into two segments 3 cm3 cm from the base, what would the surface area of the bottom segment be?