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Find the volume of a right circular cone that has a height of 4.1 cm and a base with a diam
14.8 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer Attempt 1 out of 2
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Jun 3
12:

Verified Answer :

GinnyAnswer

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.
\(\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{14.8}{2} = 7.4 \text{ cm} \]\)

3. Use the formula for the volume (V) of a right circular cone:
- The volume of a cone is given by:
\(\[ V = \frac{1}{3} \pi r^2 h \]\)
where \(\( \pi \)\) (pi) is approximately 3.14159.

4. Substitute the radius and height into the formula:
\(\[ V = \frac{1}{3} \pi (7.4)^2 (4.1) \]\)

5. Calculate the squared radius and the product:
- Squaring the radius:
\(\[ 7.4^2 = 54.76 \]\)
- Multiplying this by the height and then by \(\( \frac{1}{3} \)\):
\(\[ V = \frac{1}{3} \pi \cdot 54.76 \cdot 4.1 \]\)

6. Perform the multiplication:
\(\[ \frac{1}{3} \cdot 54.76 \cdot 4.1 \approx 74.97 \]\)
- Now, multiply this result by \(\( \pi \)\):
\(\[ V \approx 74.97 \cdot 3.14159 \approx 235.1126054044553 \text{ cm}^3 \]\)

7. Round the volume to the nearest tenth:
- The volume, when rounded to the nearest tenth, is:
\(\[ 235.1 \text{ cm}^3 \]\)

Therefore, the volume of the right circular cone is approximately 235.1 cubic centimeters when rounded to the nearest tenth.

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