To find the volume of a right circular cone given the height and diameter, follow these steps:
1. Identify the given measurements:
- The height (h) of the cone is 4.1 cm.
- The diameter of the base of the cone is 14.8 cm.
2. Calculate the radius (r) of the base:
- The radius is half of the diameter.
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{14.8}{2} = 7.4 \text{ cm}
\][/tex]
3. Use the formula for the volume (V) of a right circular cone:
- The volume of a cone is given by:
[tex]\[
V = \frac{1}{3} \pi r^2 h
\][/tex]
where [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
4. Substitute the radius and height into the formula:
[tex]\[
V = \frac{1}{3} \pi (7.4)^2 (4.1)
\][/tex]
5. Calculate the squared radius and the product:
- Squaring the radius:
[tex]\[
7.4^2 = 54.76
\][/tex]
- Multiplying this by the height and then by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[
V = \frac{1}{3} \pi \cdot 54.76 \cdot 4.1
\][/tex]
6. Perform the multiplication:
[tex]\[
\frac{1}{3} \cdot 54.76 \cdot 4.1 \approx 74.97
\][/tex]
- Now, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[
V \approx 74.97 \cdot 3.14159 \approx 235.1126054044553 \text{ cm}^3
\][/tex]
7. Round the volume to the nearest tenth:
- The volume, when rounded to the nearest tenth, is:
[tex]\[
235.1 \text{ cm}^3
\][/tex]
Therefore, the volume of the right circular cone is approximately 235.1 cubic centimeters when rounded to the nearest tenth.
