Respuesta :
Question :-
- A Cylinder has a Height of 16 Feet and a Diameter of 22 Feet . What is its Volume ?
Answer :-
- Volume of Cylinder is 6084.5 Feet ³.
Explanation :-
As per the provided information in the given question, we have been given that the Height of Cylinder is 16 feet and the Diameter is given as 22 feet . And, we have been asked to calculate the Volume of Cylinder .
For calculating the Volume , first we need to find Radius of Cylinder .
Here, we will find the Radius :-
[tex] \bigstar \: \: \boxed{ \sf{ \: Radius \: = \: \dfrac{Diameter}{2} \: }} [/tex]
[tex] \longmapsto \: \: \sf { Radius \: = \: \dfrac{ \: 22 \: }{2} \: } [/tex]
[tex] \longmapsto \: \: \bf { Radius \: = \: 11 \: Feet } [/tex]
Now, we will find Volume of Cylinder :-
[tex] \bigstar \: \: \boxed{ \sf{ \: Volume \: _{Cylinder} \: = \: \pi r^{2} h \: }} [/tex]
[tex] \longmapsto \: \: \sf {Volume \: _{Cylinder} \: = \: \dfrac{22}{7} \: \times \: ({11})^{2} \: \times \: 16 } \\ [/tex]
[tex] \longmapsto \: \: \sf {Volume \: _{Cylinder} \: = \: \dfrac{22}{7} \: \times \: 121 \: \times \: 16 } \\ [/tex]
[tex] \longmapsto \: \: \sf {Volume \: _{Cylinder} \: = \: \dfrac{22}{7} \: \times \: 1936 } \\ [/tex]
[tex] \longmapsto \: \: \sf {Volume \: _{Cylinder} \: = \: \dfrac{22 \: \times \: 1936}{7}} \\ [/tex]
[tex] \longmapsto \: \: \sf {Volume \: _{Cylinder} \: = \: \dfrac{ \: 42592 \:}{7}} \\ [/tex]
[tex] \longmapsto \: \: \bf {Volume \: _{Cylinder} \: = \: 6084.5 \: Feet^{3}} [/tex]
[tex] \underline {\rule {180pt} {4pt}} [/tex]
Formula Used :-
[tex] \Longrightarrow \: \: \boxed{ \sf{ \: Volume \: _{Cylinder} \: = \: \pi r^{2} h \: }} [/tex]
Where ,
- R denotes to the Radius
- H denotes to the Height
Given:
- Height= 16 feet
- Diameter= 22 feet
To find:
The volume of the given cylinder.
Solution:
[tex]v = \pi {r}^{2} h[/tex]
[tex]v = \pi \times {11}^{2} \times 16[/tex]
[tex]v = 6082.12338 \: {ft}^{3} [/tex]
[tex]v = 6082.12 \: {ft}^{3} (2 \: dp)[/tex]
Therefore, the volume of the given cylinder is 6082.12 cubic feets.
