1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Assertion (A) The area of the quadrant of a circle having a circumference of 22 cm is $9\frac{5}{8}{\mathrm{cm}}^{2}.$ Reason (R) The area of a sector of a circle of radius r with central angle x° is $\left(\frac{x×\mathrm{\pi }{r}^{2}}{360}\right).$ (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) Reason (R) true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

Open in App
Solution

## (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Assertion (A): Let r be the radius of the circle. Now, Circumference of the circle $=2\mathrm{\pi }r\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$ We have: $2\mathrm{\pi }r=22\phantom{\rule{0ex}{0ex}}⇒2×\frac{22}{7}×r=22\phantom{\rule{0ex}{0ex}}⇒r=\left(22×\frac{7}{44}\right)\mathrm{cm}\phantom{\rule{0ex}{0ex}}⇒r=\frac{7}{2}\mathrm{cm}$ Area of the quadrant$=\frac{90°}{360°}\mathrm{\pi }{r}^{2}$ $=\left(\frac{1}{4}×\frac{22}{7}×\frac{7}{2}×\frac{7}{2}\right){\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}=\frac{77}{8}{\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}=9\frac{5}{8}{\mathrm{cm}}^{2}$ Hence, assertion (A) is true. Reason (R): The given statement is true. Assertion (A) is true and reason (R) is the correct explanation of assertion (A).

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Area of a Sector
MATHEMATICS
Watch in App
Join BYJU'S Learning Program