[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]
Given :-
- The height of the cylinder is 26 cm
- The base of the cylinder is 12cm
- The base diameter of hemisphere is 12cm
To Find :-
- We have to find the volume of composite solid.
Let's Begin :-
For cylinder,
- Height = 26 cm
- Base diameter = 12cm
Therefore,
The radius of the cylinder will be
[tex]\sf{=} {\sf{\dfrac{ Diameter}{2}}}[/tex]
[tex]\sf{=}{\sf{\dfrac{ 12}{2}}}[/tex]
[tex]\sf{ = 6 cm}[/tex]
Thus, The radius of cylinder is 6 cm
Now, we know that,
Volume of cylinder = πr²h
Subsitute the required values,
[tex]\sf{ = 3.14 × 6 × 6 × 26}[/tex]
[tex]\sf{ = 2939.04 cm³}[/tex]
Now, For Hemisphere
Therefore,
The radius of the hemisphere will be
[tex]\sf{=} {\sf{\dfrac{ Diameter}{2}}}[/tex]
[tex]\sf{=}{\sf{\dfrac{ 12}{2}}}[/tex]
[tex]\sf{ = 6 cm}[/tex]
We know that,
Volume of hemisphere = 2/3πr³
Subsitute the required values,
[tex]\sf{ = 2/3× 3.14 × 6 × 6 × 6}[/tex]
[tex]{\sf{=}}{\sf{\dfrac{ 1356.48}{3}}}[/tex]
[tex]\sf{ = 452.16 cm³}[/tex]
Thus, The volume of hemisphere is 452.16 cm³
Therefore ,
Area of composite solid
[tex]\sf{ = 2939.04 + 452.16}[/tex]
[tex]\sf{ = 3391.2 cm³}[/tex]
[tex]\sf{ = 3391 cm³}[/tex]
Hence, The total volume of composite solid is 3391 cm³
