Question

A cone has a height of `15 cm` and its base has a radius of `8 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?

Answer 1

`579.047\ \text{cm}^2`

Explanation:

Radius `r` of new circular section of bottom segment cut horizontally, at a height `h=8\ cm` from base, from a original cone of height `H=15\ cm` & base radius `R=8\ cm` by using property of similar triangle we get

`\frac{R-r}{h}=\frac{R}{H}`

`r=R(1-\frac{h}{H})`

`=8(1-8/15)`

`=3.733\ cm`

Now, surface area of bottom segment of original cone

`=\text{area of circular top of radius 3.733}+\text{curved surface area of frustum of cone}+\text{area of circular base of radius 8}`

`=\pir^2+\pi(r+R)\sqrt{h^2+(R-r)^2}+\piR^2`

`=\pi(3.733)^2+\pi(3.733+8)\sqrt{8^2+(8-3.733)^2}+\pi(8)^2`

`=579.047\ \text{cm}^2`