Question

A cone has a height of `14 cm` and its base has a radius of `7 cm`. If the cone is horizontally cut into two segments `5 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of the bottom segment = 419.6876 sq. cm.

Explanation:

`(r1)/(h1)=(r2)/(h2)`
`7/14=(r2)/9`
`r2=9/2`

`l1=sqrt((r1)^2+(h1)^2)=sqrt(7^2+14^2)=7sqrt5`
Lateral surface area of bigger one `=(pi)*r1*l1=(22/7)*7*7sqrt5`
`=154sqrt5=344.3545`

`l2=sqrt((r2)^2+(h2)^2)=sqrt((9/2)^2+9^2)=(9/2)sqrt(5)`
Lateral surface area of smaller cone
`=(pi)*r2*l2`
`=(22*9*9sqrt5)/(7*2*2)`
`=(891/14)sqrt5=142.3098`

Lateral surface area of the bottom segment
`=344.3545-142.3098=202.0447`

Area of larger base `=(22*7*7)/7=154`

Area of smaller base `=(22*9*9)/(7*2*2)=891/14=63.6429`

Surface area of the bottom segment
`=202.0447+154+63.6429= **419.6876**`cm^2#