Question

A cone has a surface area of `600π cm^2` and a base area of `225π cm^2`. Calculate: the apothem and volume of the cone?

Answer 1

Apothem is `25` `cm.` and volume of cone is `1500pi` `cm^3`.

Explanation:

In a cone whose radius at base is `r` and height is `h`, its apothem is `a=sqrt(r^2+h^2)`.

While base area in such case is `pir^2` and curved surface area is `pira`. Therefore its total surface area is `pir(r+a)` and volume is `1/3pir^2h`

As given cone has a base area of `225pi` `cm^2`

`pir^2=225pi` and `r=sqrt225=15` `cm.`

As total surface are is `600pi` `cm^2`, we have

`pir(r+a)=600pi` or `15(15+a)=600`

i.e. `15+a=40` and `a=40-15=25` `cm.` and

`h=sqrt(25^2-15^2)=sqrt(625-225)=sqrt400=20` `cm`.

and volume of cone is `1/3pixx15xx15xx20`

= `5xx15xx20pi=1500pi` `cm^3`.