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Answer :
To find the volume of a right circular cone with a height of 6.2 inches and a base with a radius of 12.4 inches, we use the formula for the volume of a cone:
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height, and
- [tex]\( \pi \)[/tex] is approximately 3.14159.
Let's go through the steps:
1. Identify the given values:
- Radius ([tex]\( r \)[/tex]) = 12.4 inches
- Height ([tex]\( h \)[/tex]) = 6.2 inches
2. Plug these values into the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \times \pi \times (12.4)^2 \times 6.2 \][/tex]
3. Calculate the area of the base ([tex]\( \pi r^2 \)[/tex]):
[tex]\[ \pi \times (12.4)^2 = \pi \times 153.76 \approx 483.9634 \][/tex] (using [tex]\( \pi \approx 3.14159 \)[/tex])
4. Find the volume by multiplying by the height and dividing by 3:
[tex]\[ \text{Volume} = \frac{1}{3} \times 483.9634 \times 6.2 \approx 998.306 \][/tex]
5. Round to the nearest tenth:
- The volume of the cone is approximately 998.3 cubic inches.
Therefore, the volume of the cone is approximately 998.3 cubic inches.
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height, and
- [tex]\( \pi \)[/tex] is approximately 3.14159.
Let's go through the steps:
1. Identify the given values:
- Radius ([tex]\( r \)[/tex]) = 12.4 inches
- Height ([tex]\( h \)[/tex]) = 6.2 inches
2. Plug these values into the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \times \pi \times (12.4)^2 \times 6.2 \][/tex]
3. Calculate the area of the base ([tex]\( \pi r^2 \)[/tex]):
[tex]\[ \pi \times (12.4)^2 = \pi \times 153.76 \approx 483.9634 \][/tex] (using [tex]\( \pi \approx 3.14159 \)[/tex])
4. Find the volume by multiplying by the height and dividing by 3:
[tex]\[ \text{Volume} = \frac{1}{3} \times 483.9634 \times 6.2 \approx 998.306 \][/tex]
5. Round to the nearest tenth:
- The volume of the cone is approximately 998.3 cubic inches.
Therefore, the volume of the cone is approximately 998.3 cubic inches.
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