UPSC CDS 2 2018 Math Paper

Let the radius of semi–circular plate be R and radius of cone be r.
Circumference of base of cone = 2πr
2πr=πR⇒r=

R

2

Slant height of cone = R
In Δ ABC :
sin‌θ=

BC

AC

=

R 2

R

=

1

2

⇒t=30°
∴ Angle between axis and generator of cone = 30°.