| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion The area of a circular playground is\[22176\text{ }{{m}^{2}}\], the cost of fencing this ground at the rate of Rs 50 per m is Rs 26400. |
| Reason If R and r be the radius of outer and inner circular path, then area of the ring will be\[\pi \,\left( {{R}^{2}}-{{r}^{2}} \right)\]. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is false.
D) A is false; R is true.
Correct Answer: B
Solution :
Given, area of a circular playground \[=22176\,{{m}^{2}}\] \[\therefore \,\,\pi {{r}^{2}}=22176\] [\[\because \] area of circle \[=\pi {{r}^{2}}\]] \[\Rightarrow \,\,\,\frac{22}{7}{{r}^{2}}=22176\,\Rightarrow {{r}^{2}}=1008\times 7\] \[\Rightarrow \,\,\,\,{{r}^{2}}=7056\Rightarrow \,r=84\,m\] \[\therefore \]Circumference of a circle \[=2\pi r=2\times \frac{22}{7}\times 84\] \[=44\times 12=528\,m\] \[\therefore \]Cost of fencing this ground \[=\text{ }528\times 50\text{ }=Rs26400\]
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