To find the volume of a right circular cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( \pi \approx 3.14 \)[/tex], [tex]\( r \)[/tex] is the radius of the base, and [tex]\( h \)[/tex] is the height of the cone.
1. Given Data:
- Diameter of the base of the cone, [tex]\( \text{diameter} = 4 \)[/tex] inches.
- Height of the cone, [tex]\( h = 6 \)[/tex] inches.
2. Calculate the Radius:
The radius [tex]\( r \)[/tex] is half of the diameter:
[tex]\[ r = \frac{\text{diameter}}{2} \][/tex]
[tex]\[ r = \frac{4}{2} = 2 \text{ inches} \][/tex]
3. Calculate the Volume:
Substitute the known values into the volume formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
[tex]\[ V = \frac{1}{3} \times 3.14 \times (2^2) \times 6 \][/tex]
[tex]\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \][/tex]
[tex]\[ V = \frac{1}{3} \times 3.14 \times 24 \][/tex]
[tex]\[ V = \frac{1}{3} \times 75.36 \][/tex]
[tex]\[ V = 25.12 \text{ in}^3 \][/tex]
4. Round to the Nearest Tenth:
The volume is approximately:
[tex]\[ V \approx 25.1 \text{ in}^3 \][/tex]
Therefore, the volume of the cone is:
[tex]\[ \boxed{25.1 \text{ in}^3} \][/tex]
