The curved surface area of a right circular cone is `sqrt(2)` times of the area of the base. Then what is the vertical angle of the cone ?

Explanation

Let the radius of the base of the right circular cone be r unit and its slant height be l unit .
As per question, `pi r l = sqrt(2)pir^2rArr l=sqrt(2)r`
Now , let the semi - vertical angle be `theta`.
`therefore` from the right - angled `Delta AOB ` we get , `(OB)/(AB)=sinthetarArr sintheta=(r)/(sqrt(2r))=(1)/(sqrt(2))`
`B=sin45^@rArr theta=45^@`.
Hence the vertical angle `=2xx45^@=90^@`.