text: # 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; ?>
explanation: The document contains a geometry question about finding the volume of a wooden door wedge in the shape of a sector of a circle. It also includes the correct answer and a detailed solution.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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; ?>
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a geometry question about finding the volume of a wooden door wedge in the shape of a sector of a circle. It also includes the correct answer and a detailed solution.
  
  Label: question-and-answer