Geometry and Mensuration: Test 10

$\begin{array}{l}2\pi r=132\\\Rightarrow r=21cm\\Side\,\,of\,\,the\,\,square=21cm\\Length\,\,of\,\,the\,\,rec\tan gle=\frac{3}{5}\times 21=12.6cm\\Breadth=8cm\\Area=12.6\times 8=100.8c{{m}^{2}}\end{array}$

$\displaystyle \begin{array}{l}Side\text{ }of\text{ }{{1}^{st}}square\text{ }=\text{ }56/4\text{ }=\text{ }14\text{ }cm.\\Smallest\text{ }side\text{ }of\text{ }right\text{ }angled\text{ }triangle=\text{ }14\text{ }-8~=\text{ }6\text{ }cm.\\length\text{ }of\text{ }{{2}^{nd}}rectangle\text{ }=\text{ }96/8\text{ }=\text{ }12\text{ }cm.\\Second\text{ }largest\text{ }side\text{ }of\text{ }the\text{ }{{1}^{st}}rectangle\text{ }=~12-4\text{ }=\text{ }8\text{ }cm.\\largest\text{ }side\text{ }=\text{ }hypotenuse=\sqrt{{{8}^{2}}+{{6}^{2}}}=10cm~\end{array}$

Total volume displaced by men = 150X 8 = 1200 cu. m.
Area of the surface of swimming pool = 90m X 40m = 3600 sq.m.
Rise in water level = 1200/3600 m = 1/3 th of a metre = 33.33 cm

Total surface area of 4 cm cube= 6a²
=6 x 4 x 4 = 96cm²
Number of new cubes = 4³/1³ = 64
Total surface area of new cube = 64x6x1² = 384cm²
Increase = 384-96 = 288
Increase Percentage = 288/96 x 100 = 300%

$\displaystyle \begin{array}{l}The\text{ }lateral\text{ }length=\sqrt{{{12}^{2}}+{{5}^{2}}}=13m\\Lateral\text{ }surface\text{ }area=\pi \times r\times l\\=\pi \times 5\times 13=65\pi {{m}^{2}}\end{array}$