In the following diagram a rectangular platform with a semicircular end on one side is 22 meters long from one end to the other end. If the length of the half circumference is 11 meters, find the cost of constructing the platform, 1.5 meters high at the rate of Rs 4 per cubic meters.

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

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(G) - 2

Length of the platform = 22 m

Circumference of semi-circle (c) = 11 m

$\begin{array}{*{35}{l}} radius\text{ }=\text{ }\left( c\text{ x }2 \right)/\text{ }\left( 2\text{ x }\pi \right)\text{ }=\text{ }\left( 11\text{ x }7 \right)/\text{ }22\text{ }=\text{ }7/2\text{ }m \\ ~the\text{ }breadth\text{ }of\text{ }the\text{ }part\text{ }=\text{ }7/2\text{ x }2\text{ }=\text{ }7\text{ }m \\ length\text{ }=\text{ }22\text{ }\text{ }7/2\text{ }=\text{ }37/2\text{ }=\text{ }18.5\text{ }m \\ area\text{ }of\text{ }platform\text{ }=\text{ }l\text{ x }b\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }\pi {{r}^{2}} \\ =\text{ }18.5\text{ x }7\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ x }22/7\text{ x }7/2\text{ x }7/2\text{ }{{m}^{2}} \\ =\text{ }129.6\text{ }+\text{ }77/4\text{ }{{m}^{2}} \\ =\text{ }148.75\text{ }{{m}^{2}} \\ \end{array}$

height of the platform = 1.5 m

$~the\text{ }volume\text{ }=\text{ }148.75\text{ x }1.5\text{ }=\text{ }223.125\text{ }{{m}^{3}}$

Rate of construction = Rs 4 per m³

$Total\text{ }expenditure\text{ }=\text{ }Rs\text{ }4\text{ x }223.125\text{ }=\text{ }Rs\text{ }892.50$

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