A piece of paper in the shape of a sector of a circle (see Fig. 1) is rolled up to form a right-circular cone (see Fig. 2). The value of the angle θ is

Question

A piece of paper in the shape of a sector of a circle (see Fig. 1) is rolled up to form a right-circular cone (see Fig. 2). The value of the angle θ is (A) (10 π/13) (B) (9 π/13) (C) (5 π/13) (D) (6 π/13)

Tardigrade Admin · Accepted Answer

We know, θ=(A B/O B) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d41995634d2947daa1e2311e7a66be5b-.png" /> From first figure, A B =2 π r O B =13 ∴ 2 π(5) =13 θ ⇒ θ=(10 π/13)

Q. A piece of paper in the shape of a sector of a circle (see Fig. $1$ ) is rolled up to form a right-circular cone (see Fig. $2$ ). The value of the angle $θ$ is

$\frac{10 π}{13}$

$\frac{9 π}{13}$

$\frac{5 π}{13}$

$\frac{6 π}{13}$

We know, $θ = \frac{A B}{OB}$

From first figure,
$A B = 2 π r$
$OB = 13$
$∴ 2 π (5) = 13 θ$
$\Rightarrow θ = \frac{10 π}{13}$

Q. A piece of paper in the shape of a sector of a circle (see Fig. 1) is rolled up to form a right-circular cone (see Fig. 2). The value of the angle θ is

1310π​

139π​

135π​

136π​