A sector of a circle of radius \(15 \mathrm{~cm}\) subtending an angle of \(200^{\circ}\) at the centre of the circle is bent to form a cone. find the base radius of the cone so formed.
A. \(3.88 \mathrm{~cm}\) B. \(8.33 \mathrm{~cm}\) C. \(2.55 \mathrm{~cm}\) D. \(5.22 \mathrm{~cm}\) E. B
Correct Answer:
Explanation
S.A + area of base circle \(=\pi l+\pi r^{2}\) Sector of a circle Cone formed given: \(R=15 \mathrm{~cm} . \theta=200^{\circ}\) we are to find \(r=\) ? using the relationship that the length of the arc equals circumference of the base of the cone i.e. length of \(\operatorname{arc} l=\frac{\theta}{360} \times 2 \pi R\) circumference of base of cone \(=2 \pi \mathrm{r}\) thus \begin{aligned} \frac{\theta}{360} \times 2 \pi R &=2 \pi r \\ r &=\frac{R \theta}{360}, \\ r &=\frac{15 \times 200}{360}=\frac{300}{36} \\ &=8.33 \mathrm{~cm} \end{aligned}