Geometry and Mensuration: Test 9

$\displaystyle \begin{array}{l}Let\text{ }the\text{ }two\text{ }circles\text{ }be\text{ }of\text{ }radii\text{ }r\text{ }and\text{ }R\text{ }cm\text{ }respectively.\\2\pi r=88\\r=14cm\\and\,\,2\pi R=220\\R=35cm\\Difference\text{ }in\text{ }area=\pi \left( {{R}^{2}}-{{r}^{2}} \right)=\frac{22}{7}\times 49\times 21=3234c{{m}^{2}}\end{array}$

$\displaystyle \begin{array}{l}Side\text{ }of\text{ }the\text{ }square~=\text{ }112/4\text{ }=\text{ }28\text{ }m.\\Area\,\,of\,\,circle\,\,\,=\pi \times {{28}^{2}}=\frac{22}{7}\times 28\times 28=2464{{m}^{2}}\\Correct\,\,option\,\,is\,\,e\end{array}$

$\displaystyle \begin{array}{l}Area\text{ }of\text{ }the\text{ }circle=\pi \times {{14}^{2}}=196\times \frac{22}{7}=616c{{m}^{2}}\\Area\text{ }of\text{ }rectangle=1166-616=550c{{m}^{2}}\\Length\text{ }of\text{ }rectangle=25cm\\Thus\,breadth=\frac{550}{25}=22cm\\Sum\,\,of\,\,perimeter=2\pi r+2\left( 25+22 \right)\\=(2\pi \times 14)+94=182cm\end{array}$

$\begin{array}{l}2\pi r+4a=272\\\Rightarrow a=\frac{1}{4}\left( 272-176 \right)\\=\frac{1}{4}\times 96cm=24cm\\Sum\text{ }of\text{ }the\text{ }area=\pi {{r}^{2}}+{{a}^{2}}=2464+576=3040\end{array}$