A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.

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

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(F) - 5

Diameter of cylindrical boiler = 3.5 m

So, the radius (r) = 3.5/2 = 35/20 = 7/4 m

Height (h) = 2m

Radius of hemisphere (R) = 7/4 m

$\begin{array}{*{35}{l}} Total\text{ }volume\text{ }of\text{ }the\text{ }boiler\text{ }=\text{ }\pi {{r}^{2}}h\text{ }+\text{ }2/3\text{ }\pi {{r}^{3}} \\ =\text{ }\pi {{r}^{2}}\left( h\text{ }+\text{ }2/3r \right) \\ =\text{ }22/7\text{ x }7/4\text{ x }7/4\text{ }\left( 2\text{ }+\text{ }2/3\text{ x }7/4 \right) \\ =\text{ }77/8\text{ }\left( 2\text{ }+\text{ }7/6 \right) \\ =\text{ }77/8\text{ x }19/6\text{ }=\text{ }1463/48 \\ =\text{ }30.48\text{ }{{m}^{3}} \\ \end{array}$

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