Answer :
To determine the volume of a cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Here:
- [tex]\( V \)[/tex] is the volume of the cone
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14
- [tex]\( r \)[/tex] is the radius of the base of the cone
- [tex]\( h \)[/tex] is the height of the cone
Given:
- The height [tex]\( h \)[/tex] of the cone is 10 meters
- The base diameter [tex]\( d \)[/tex] of the cone is 12 meters
First, we need to find the radius [tex]\( r \)[/tex]. The radius is half of the diameter:
[tex]\[ r = \frac{d}{2} = \frac{12\, \text{m}}{2} = 6\, \text{m} \][/tex]
Now, substitute the values into the volume formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
[tex]\[ V = \frac{1}{3} \times 3.14 \times (6\, \text{m})^2 \times 10\, \text{m} \][/tex]
Let's calculate step-by-step:
1. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = 6\, \text{m} \times 6\, \text{m} = 36\, \text{m}^2 \][/tex]
2. Multiply [tex]\( r^2 \)[/tex] by [tex]\( h \)[/tex]:
[tex]\[ r^2 \times h = 36\, \text{m}^2 \times 10\, \text{m} = 360\, \text{m}^3 \][/tex]
3. Multiply by [tex]\( \pi \)[/tex]:
[tex]\[ \pi \times 360\, \text{m}^3 = 3.14 \times 360\, \text{m}^3 = 1130.4\, \text{m}^3 \][/tex]
4. Finally, divide by 3:
[tex]\[ V = \frac{1130.4\, \text{m}^3}{3} = 376.8\, \text{m}^3 \][/tex]
So, the volume of the cone is:
[tex]\[ \boxed{376.8\, \text{m}^3} \][/tex]
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Here:
- [tex]\( V \)[/tex] is the volume of the cone
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14
- [tex]\( r \)[/tex] is the radius of the base of the cone
- [tex]\( h \)[/tex] is the height of the cone
Given:
- The height [tex]\( h \)[/tex] of the cone is 10 meters
- The base diameter [tex]\( d \)[/tex] of the cone is 12 meters
First, we need to find the radius [tex]\( r \)[/tex]. The radius is half of the diameter:
[tex]\[ r = \frac{d}{2} = \frac{12\, \text{m}}{2} = 6\, \text{m} \][/tex]
Now, substitute the values into the volume formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
[tex]\[ V = \frac{1}{3} \times 3.14 \times (6\, \text{m})^2 \times 10\, \text{m} \][/tex]
Let's calculate step-by-step:
1. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = 6\, \text{m} \times 6\, \text{m} = 36\, \text{m}^2 \][/tex]
2. Multiply [tex]\( r^2 \)[/tex] by [tex]\( h \)[/tex]:
[tex]\[ r^2 \times h = 36\, \text{m}^2 \times 10\, \text{m} = 360\, \text{m}^3 \][/tex]
3. Multiply by [tex]\( \pi \)[/tex]:
[tex]\[ \pi \times 360\, \text{m}^3 = 3.14 \times 360\, \text{m}^3 = 1130.4\, \text{m}^3 \][/tex]
4. Finally, divide by 3:
[tex]\[ V = \frac{1130.4\, \text{m}^3}{3} = 376.8\, \text{m}^3 \][/tex]
So, the volume of the cone is:
[tex]\[ \boxed{376.8\, \text{m}^3} \][/tex]
