Question

Find the volume of a right circular cone obtained from a sector of a circle in which the radius is 26 cm and the central angle is 138.5 ° ? Round your final answer to 1 decimal place.

Answer 1

$\displaystyle \textsf{Slant height of cone} = \\ \textsf{Radius of circle which a sector is cut from.}\\ l = 26cm\\ \textsf{Circumference of base of cone} = \textsf{length of arc}\\ 2\pi R = \frac{138.5\degree}{360\degree} \times 2\pi \times 26\\ R = \frac{3601}{360}\,cm\\ \begin{aligned} V &= \frac{1}{3}\pi R^2 \sqrt{l^2 - R^2} \\&= \frac{\pi}{3}\left(\frac{3601}{360}\right)^2 \times \sqrt{26^2 - \left(\frac{3601}{360}\right)^2} \\&= 2514.5\,cm^3 \,(1 \,\textsf{d.p.}) \end{aligned}$