| An umbrella has 8 ribs which are equally spaced (see the figure). |
| Assuming umbrella to be a flat circle of radius 45 cm, then the area between the two consecutive ribs of the umbrella is |
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A) \[\frac{22275}{56}\,c{{m}^{2}}\]
B) \[\frac{22275}{28}\,c{{m}^{2}}\]
C) \[\frac{22285}{28}\,c{{m}^{2}}\]
D) None of these
Correct Answer: B
Solution :
Given, umbrella to be a flat circle. So, the central angle of an umbrella is \[360{}^\circ \]. Since, umbrella has 8 ribs. \[\therefore \] Angle between two ribs \[=\frac{360{}^\circ }{8}=45{}^\circ \] Area between two ribs = Area of one sector of the umbrella \[=\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}=\frac{45{}^\circ }{360{}^\circ }\times \frac{22}{7}\times {{\left( 45 \right)}^{2}}\] \[\left[ \because \,\,r=45,\,given \right]\] \[=\frac{22}{7\times 8}\times 45\times 45=\frac{22275}{28}c{{m}^{2}}\]
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