Question

Curved surface area of a conical cup is 308 cm square and base radius is 7 cm . Find the angle at the vertex of the cone the vertex of the cone.

Answer 1

The vertex angle is 60°

Explanation:

Curved surface area of cone $=\pi rl$

where r is radius and l is slant height.

$\pi rl=308$

$\pi\times 7 \times l=308$

$l=14$

Let vertex angle be Ф

$\sin\dfrac{\theta}{2}=\dfrac{r}{l}$

$\sin\dfrac{\theta}{2}=\dfrac{7}{14}$

$\sin\dfrac{\theta}{2}=\dfrac{1}{2}$

$\sin\dfrac{\theta}{2}=\sin30^\circ$

$\theta=60^\circ$

#BAL

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