Question

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 `2 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `129.56` sq.cm.

Explanation:

The cone is cut at 2 cm from base, So upper radius of the frustum

of cone is `r_2=(9-2)/9*4=28/9~~ 3.11` cm. Slant height:

`l=sqrt(2^2+(4-3.11)^2)=sqrt(4+0.79)=sqrt 4.79~~2.19`

Top surface area `A_t=pi*3.11^2 ~~30.39` sq.cm

Bottom surface area `A_b=pi*4^2 ~~50.27` sq.cm

Slant Area `A_s=pi*l*(r_1+r_2)=pi*2.19*(4+3.11)~~48.9`

sq.cm. Total surface area of bottom segment is

`A=A_t+A_b+A_s=30.39+50.27+48.9=129.56 (2dp)`

sq.cm

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