# Moderate Geometry & Mensuration Solved QuestionAptitude Discussion

 Q. A wooden door wedge is in the shape of a sector of a circle of radius 10 cm with angle $24^\circ$ and constant thickness 3 cm. Find the volume of wood used in making the wedge.
 ✔ A. $62.83\text{ cm}^3$ ✖ B. $57.88\text{ cm}^3$ ✖ C. $41.22\text{ cm}^3$ ✖ D. $33.15\text{ cm}^3$

Solution:
Option(A) is correct

The area of the top face of the wedge is the area of a sector of radius 10 cm and angle $24^\circ$

\begin{align*} \text{Area}&=\dfrac{24^\circ}{360^\circ}\times \pi \times 10^2\\ &=\dfrac{20\pi}{3}\\ &=20.94\text{ cm}^2 \end{align*}

The volume of the wedge

\begin{align*} &=\text{Area}\times 3\\ &=20\pi\\ &=62.83\text{ cm}^3 \end{align*}