| The total area of a circle and a rectangle is equal to \[1166\,c{{m}^{2}}.\] The diameter of the circle is 28 cm. What is the sum of the circumference of the circle and the perimeter of the rectangle, if the length of the rectangle is 25 cm? |
A) 186 cm
B) 182 cm
C) 184 cm
D) Cannot be determined
E) None of the above
Correct Answer: B
Solution :
| The area of the circle \[=\pi {{r}^{2}}\] |
| \[=\frac{22}{7}\times 14\times 14=616\,c{{m}^{2}}\] [\[\because \] diameter = 28] |
| Let the length and breadth of the rectangle be x cm and y cm, respectively. |
| Then, \[x\times y=1166-616\] |
| \[\Rightarrow \] \[25\times y=550\]\[\Rightarrow \]\[y=\frac{550}{25}=22\,cm\] |
| \[\therefore \] Perimeter of the rectangle\[=2\,(x+y)\] |
| \[=2\,(25+22)=94\,cm\] |
| and circumference of the circle \[=2\pi r\] |
| \[=2\times \frac{22}{7}\times 14=88\,cm\] |
| Hence, required sum \[=94+88=182\,cm\] |
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