The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the following figure.The tunnel is 80 m long. Calculate:(iii) its floor area

Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20G | ICSE | Selina

FIGURE:

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(G) - 3

Side of square (a) = 7m

the radius of semi-circle = 7/2 m

Length of the tunnel = 80 m

$\begin{array}{*{35}{l}} Area\text{ }of\text{ }cross\text{ }section\text{ }of\text{ }the\text{ }front\text{ }part\text{ }=\text{ }{{a}^{2}}~+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }\pi {{r}^{2}} \\ =\text{ }7\text{ }x\text{ }7\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }x\text{ }22/7\text{ }x\text{ }7/2\text{ }x\text{ }7/2 \\ =\text{ }49\text{ }+\text{ }77/4\text{ }{{m}^{2}} \\ =\text{ }\left( 196\text{ }+\text{ }77 \right)/\text{ }4 \\ =\text{ }273/4\text{ }{{m}^{2}} \\ \end{array}$

$\left( iii \right)\text{ }Area\text{ }of\text{ }floor\text{ }=\text{ }l\text{ }x\text{ }b\text{ }=\text{ }7\text{ }x\text{ }80\text{ }=\text{ }560\text{ }{{m}^{2}}$

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