Geometry & Mensuration

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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.


\(62.83\text{ cm}^3\)


\(57.88\text{ cm}^3\)


\(41.22\text{ cm}^3\)


\(33.15\text{ cm}^3\)

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Option(A) is correct

Answer image for Mensuration, Aptitude:2173-1

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 

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

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