Question

A cone has a height of `18 cm` and its base has a radius of `9 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?

Answer 1

Surface area `~~148.833cm^2`

Explanation:

For a really detailed explanation of how to solve questions like these, check out my other similar answers at

https://socratic.org/questions/a-cone-has-a-height-of-16-cm-and-its-base-has-a-radius-of-3-cm-if-the-cone-is-ho-1#478093 and

https://socratic.org/questions/a-cone-has-a-height-of-16-cm-and-its-base-has-a-radius-of-8-cm-if-the-cone-is-ho-1#476669

`R_2` equals
`18/3=3/R_2`
`18R_2=9`
`R_2=9/18=1/2=0.5`

`s` equals
`s=sqrt((3-0.5)^2+3^2)`
`s=sqrt(6.25+9)`
`s=sqrt(15.25)`

Surface area equals
`A_s=pi(sqrt15.25(3-0.5)+3^2+0.5^2)`
`A_s=pi(38.125+9+0.25)`
`A_s=pi(47.375)`
`A_s~~148.833cm^2`,
Therefore the surface area of the bottom cone segment is roughly 148.833`cm^2`.

I hope I helped!