A semi circular plate is rolled up to form a conical surface The angle between the generator and the...........

Quantitative Aptitude (CDS) Coordinate Geometry

A semi-circular plate is rolled up to form a conical surface. The angle between the generator and the axis of the cone is

60^o

45^o

30^o

15^o

Let radius of semi-circle = R
Perimeter of semi circle = circumference of base of cone

$\small \pi R= 2 \pi R$

R = 2r

$\small In\: \Delta\: ABC$

$\small \frac{BC}{AC} = Sin \theta$

$\small \frac{r}{R} = Sin \theta$

$\small \frac{r}{2r} = Sin \theta$

$\small Sin \theta = \frac{1}{2}$

$\small \theta\: = 30^{o}$

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