10th Class Mathematics Areas Related to Circles Question Bank Case Based (MCQs) - Areas Related to Circles

  • question_answer
    The relation between area of a sector A length of the arc \[l,\] angle \[\theta \] subtended by the arc at the centre and radius of circle, is:

    A) \[\frac{1}{2}lr\]

    B) \[lr\]

    C) \[\frac{1}{3}lr\]

    D) \[\frac{1}{2}l{{r}^{2}}\]

    Correct Answer: A

    Solution :

    The area of sector is given by \[A=\frac{\theta }{360}\times \pi {{r}^{2}}\]and length of the arc is given by \[l=\frac{\theta }{360}\times 2\pi \]
    Multiplying and dividing A by 2, we get
    \[A=\frac{1}{2}\times \frac{\theta }{360}\times 2\times \pi {{r}^{2}}=\frac{1}{2}\times \left( \frac{\theta }{360}\times 2r \right)\times r=\frac{1}{2}\times l\times r\]So, option [a]is correct.           

You need to login to perform this action.
You will be redirected in 3 sec spinner