Volume & Surface Area – 1

Capacity of the bank = Volume of the tank
= \(\left ( \frac{8\times100\times6\times100\times2.5\times100}{1000} \right )litres = 1210000 litres.\)

Surface area = \(\left [ 2\left ( 10\times4+4\times3+10\times3 \right ) \right ]cm^{2}= (2\times82)cm^{2}= 164 cm^{2}\)

Area of the wet surface = \(\left [ 2\left (lb+bh+lh \right )-lb \right ]= 2(bh +lh)+lb = \left [ 2\left ( 4\times1.25+6\times1.25 \right )+6\times4 \right ]m^{2}= 49 m^{2}\)

Volume of water displaced = \(\left ( 3\times2\times0.01 \right )m^{2}= 0.06m^{3}.\)
\(Mass of man = Volume of water displaced \times Density of water\)
\(=\left ( 0.06\times1000 \right )kg = 60kg\)

\(Volume = \left ( 2.6\times100\times100\times100 \right )cu. cm. Depth = \frac{Volume}{Area of the base}= \left ( \frac{2.6\times100\times100\times100}{6500} \right )cm = 400 cm = 4m.\)

Let length = x cm. Then, \(x\times28\times5\times\frac{25}{1000}= 112 \therefore x=\left ( 112\times \frac{1000}{25}\times\frac{1}{28}\times\frac{1}{5}\right )cm = 32 cm.\)

\(Area = \left ( 1.5\times10000 \right )m^{2}= 15000 m^{2} Depth = \frac{5}{100}m = \frac{1}{20}m. \therefore Volume = (Area\times Depth)=\left ( 15000\times\frac{1}{20} \right )m^{3}= 750 m^{3}\)

Let the width of the wall be x metres.
then, Height = (6x) metres and Length = (42x) metres. \(\therefore 42x\timesx\times6x = 16128 \Leftrightarrow x^{3}=\left ( \frac{16128}{42\times6} \right )= 64\Leftrightarrow x =4\)

Surface area = \(\left [ 6\times\left ( \frac{1}{2} \right )^{2} \right ]cm^{2}= \frac{3}{2}cm^{2}\)

Volume of the new cube = \(\left ( 6^{3}+8^{3}+10^{3} \right )cm^{3}= 1728 cm^{3}\)
Let the edge of the new cube be a cm.
\(\therefore a^{3}=1728 \Rightarrow a = 12\)