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Answer :
To find the volume of a right circular cone, you can use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius of the base, and [tex]\( h \)[/tex] is the height of the cone.
1. Identify the given values:
- The height ([tex]\( h \)[/tex]) of the cone is 6.2 inches.
- The radius ([tex]\( r \)[/tex]) of the base is 12.4 inches.
2. Substitute the given values into the formula:
[tex]\[ V = \frac{1}{3} \pi (12.4)^2 (6.2) \][/tex]
3. Calculate the radius squared:
[tex]\[ (12.4)^2 = 153.76 \][/tex]
4. Multiply the radius squared by the height:
[tex]\[ 153.76 \times 6.2 = 953.312 \][/tex]
5. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[ \pi \times 953.312 \approx 2994.918 \][/tex]
6. Divide by 3 (since [tex]\(\frac{1}{3}\)[/tex]):
[tex]\[ \frac{2994.918}{3} \approx 998.306 \][/tex]
7. Round to the nearest tenth:
The volume of the cone, rounded to the nearest tenth, is approximately 998.3 cubic inches.
Therefore, the volume of the cone is about 998.3 cubic inches.
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius of the base, and [tex]\( h \)[/tex] is the height of the cone.
1. Identify the given values:
- The height ([tex]\( h \)[/tex]) of the cone is 6.2 inches.
- The radius ([tex]\( r \)[/tex]) of the base is 12.4 inches.
2. Substitute the given values into the formula:
[tex]\[ V = \frac{1}{3} \pi (12.4)^2 (6.2) \][/tex]
3. Calculate the radius squared:
[tex]\[ (12.4)^2 = 153.76 \][/tex]
4. Multiply the radius squared by the height:
[tex]\[ 153.76 \times 6.2 = 953.312 \][/tex]
5. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[ \pi \times 953.312 \approx 2994.918 \][/tex]
6. Divide by 3 (since [tex]\(\frac{1}{3}\)[/tex]):
[tex]\[ \frac{2994.918}{3} \approx 998.306 \][/tex]
7. Round to the nearest tenth:
The volume of the cone, rounded to the nearest tenth, is approximately 998.3 cubic inches.
Therefore, the volume of the cone is about 998.3 cubic inches.
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