Answer:
[tex] \: [/tex]
Step-by-step explanation:
In the question, it is given that a cone has a radius of 5 meters and a height of 14 meters and we have to find the volume of the cone.
[tex] \: [/tex]
To find the volume of the cone, we must know this formula :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times \pi \times {(r)}^{2} \times h }}}}}}} \\ \\[/tex]
Where,
- r refers to the radius of the cone.
- h refers to the height of the cone.
Now, we will substitute the values in the formula :
[tex] {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 25 \times 14 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 350 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1099 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1099}{3}}}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\frak { Volume_{(cone) }= 366.33}}}}}}} \\ \\[/tex]
Therefore,
- The volume of the cone is 366.33 m³
