# 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*}

## (0) Comment(s)

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The text passage contains a geometry question about finding the volume of a wedge-shaped wooden door, and it provides the correct answer along with a detailed solution.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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*}

## (0) Comment(s)

if (defined ( 'LF_SITECTRL' )) echo LF_SITECTRL; ?>
user
The text passage contains a geometry question about finding the volume of a wedge-shaped wooden door, and it provides the correct answer along with a detailed solution.

TYPE: SINGLE_QUESTION_WITH_ANSWER