Question

cylindrical boiler 2m high is 3.5m in diameter. it has a hemispherical lid. find its internal volume include lid​

Answer 1

SOLUTION:-

Given:

•A cylindrical boiler is height= 2m.

•Their diameter is 3.5m

To find:

The interval volume & included lid.

Explanation:

Radius of the hemisphere boiler= 3.5/2

$= > \frac{3.5 \times 10}{2 \times 10} \\ \\ = > \frac{35}{20} \\ \\ = > Radius = \frac{7}{4} m$

&

Total Volume of the boiler:

$= > \pi {r}^{2} h + \frac{2}{3} \pi {r}^{ 3} \\ \\ = > \pi {r}^{2} (h + \frac{2}{3} r) \\ \\ = > \frac{22}{7} \times \frac{7}{4} \times \frac{7}{4} (2 + \frac{2}{3} \times \frac{7}{4 }) \\ \\ = > \frac{77}{8} (2 + \frac{7}{6} ) \\ \\ = > \frac{77}{8} \times \frac{19}{6} \\ \\ = > \frac{1463}{48} \\ \\ = > 30.48 {m}^{3}$

Thus,

The interval volume of the boiler is 30.48m³.

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Answer 2

Given : a cylindrical boiler 2m high is 3.5m in diameter.

it has a hemispherical lid

To Find :volume of its interior, including the part covered by the lid.

Solution :

Volume of interior = Volume of cylinder + Volume of Lid

Volume of cylinder  =  πr²h

π = 22/7

r = diameter/2 = 3.5/2 =  7/4  m

h = 2 m

Volume of cylinder  =  (22/7)(7/4)²*2

= 77/4  m³

Volume of Lid = Volume of hemisphere

hemisphere diameter would be same as cylinder

r = 7/4 m

Volume  = (2/3)πr³

= (2/3)(22/7)(7/4)³

= 539/48  m³

Total Volume = 77/4 + 539/48

=1463/48

=  30.48 m³

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