Find the volume of a right circular cone that has a height of 19.9 cm and a base with a radius of 9.6 cm. Round your answer to the nearest tenth of a cubic centimeter.
The volume of a cone is given by the formula:
\[V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h\]
where $V$ is the volume, $\pi \approx 3.14159$, $r$ is the radius of the base, and $h$ is the height.
Substituting the given values:
\[V = \frac{1}{3} \cdot \pi \cdot (9.6 \text{ cm})^2 \cdot 19.9 \text{ cm}\]
Calculating:
\[V \approx \frac{1}{3} \cdot 3.14159 \cdot (9.6 \text{ cm})^2 \cdot 19.9 \text{ cm} \approx 1831.9 \text{ cm}^3 \]
Rounding to the nearest tenth:
\[V \approx \boxed{1831.9 \text{ cm}^3}\]
try again.
Apologies for the error. Let's try again.
The volume of a cone is given by the formula:
\[V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h\]
where $V$ is the volume, $\pi \approx 3.14159$, $r$ is the radius of the base, and $h$ is the height.
Substituting the given values:
\[V = \frac{1}{3} \cdot 3.14159 \cdot (9.6 \text{ cm})^2 \cdot 19.9 \text{ cm}\]
Calculating:
\[V \approx \frac{1}{3} \cdot 3.14159 \cdot (9.6 \text{ cm})^2 \cdot 19.9 \text{ cm} \approx 1831.936 \text{ cm}^3 \]
Rounding to the nearest tenth:
\[V \approx \boxed{1831.9 \text{ cm}^3}\]
To find the volume of a right circular cone, we can use the formula:
Volume = (1/3) * π * r^2 * h
where:
π is a constant approximately equal to 3.14159
r is the radius of the base of the cone
h is the height of the cone
In this case, the height (h) is given as 19.9 cm and the radius (r) is given as 9.6 cm.
Now we can substitute these values into the formula:
Volume = (1/3) * π * (9.6 cm)^2 * 19.9 cm.
To calculate the volume, we can start by squaring the radius:
(9.6 cm)^2 = 92.16 cm^2
Next, we can multiply the squared radius by the height and the constant π:
92.16 cm^2 * 19.9 cm * (1/3) * π
Using a calculator, we can calculate the volume:
Volume ≈ 604.57 cubic cm
Rounding this to the nearest tenth of a cubic centimeter gives us:
Volume ≈ 604.6 cubic cm
Therefore, the volume of the right circular cone is approximately 604.6 cubic cm.