Answer:
The correct answer is option (C) 96π m³.
Step-by-step explanation:
As per given question we have provided that :
- ⟶ Diameter = 12 m
- ⟶ Radius = 12/2 = 6 m
- ⟶ Height = 8 m
Here's the required formula to find the volume of cone :
[tex]{\longrightarrow{\pmb{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}}[/tex]
- ➝ V = Volume
- ➝ π = 22/7
- ➝ r = radius
- ➝ h = height
Substituting all the given values in the formula to find the volume of cone :
[tex]{\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{(6)}^{2}8}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{(6 \times 6)}8}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi \times {(36)} \times 8}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \dfrac{1}{3} \times \pi \times 36 \times 8}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \dfrac{1}{\cancel{3}} \times \pi \times \cancel{36} \times 8}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \pi \times 12 \times 8}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} = \pi \times 96}}}[/tex]
[tex]{\implies{\sf{V_{(Cone)} =96\pi}}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{V_{(Cone)} =96\pi \: {m}^{3}}}}}}[/tex]
Hence, the volume of cone is 96π m³.
[tex]\rule{300}{2.5}[/tex]
