To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
Let's calculate the volume for each cone you described:
1. Cone with a diameter of 20 cm and height of 15 cm
- Diameter = 20 cm, so radius \( r = \frac{20}{2} = 10 \) cm
- Height \( h = 15 \) cm
\[ V = \frac{1}{3} \cdot 3.14 \cdot (10^2) \cdot 15 \] \[ = \frac{1}{3} \cdot 3.14 \cdot 100 \cdot 15 \] \[ = \frac{1}{3} \cdot 4710 \] \[ = 1570 \text{ cm}^3 \]
2. Oblique cone with a base radius of 9 inches and height of 5 inches
- Radius \( r = 9 \) inches
- Height \( h = 5 \) inches
\[ V = \frac{1}{3} \cdot 3.14 \cdot (9^2) \cdot 5 \] \[ = \frac{1}{3} \cdot 3.14 \cdot 81 \cdot 5 \] \[ = \frac{1}{3} \cdot 1273.7 \] \[ = 424.57 \text{ in}^3 \]
3. Chocolate mold in the shape of a cone with a diameter of 2 cm and height of 6 cm
- Diameter = 2 cm, so radius \( r = \frac{2}{2} = 1 \) cm
- Height \( h = 6 \) cm
\[ V = \frac{1}{3} \cdot 3.14 \cdot (1^2) \cdot 6 \] \[ = \frac{1}{3} \cdot 3.14 \cdot 1 \cdot 6 \] \[ = \frac{1}{3} \cdot 18.84 \] \[ = 6.28 \text{ cm}^3 \]
4. Sandcastle mold with a diameter of 4 meters and height of 6 meters
- Diameter = 4 m, so radius \( r = \frac{4}{2} = 2 \) m
- Height \( h = 6 \) m
\[ V = \frac{1}{3} \cdot 3.14 \cdot (2^2) \cdot 6 \] \[ = \frac{1}{3} \cdot 3.14 \cdot 4 \cdot 6 \] \[ = \frac{1}{3} \cdot 75.36 \] \[ = 25.12 \text{ m}^3 \]
5. Hanging flower vase with a radius of 5 inches and height of 15 inches
- Radius \( r = 5 \) inches
- Height \( h = 15 \) inches
\[ V = \frac{1}{3} \cdot 3.14 \cdot (5^2) \cdot 15 \] \[ = \frac{1}{3} \cdot 3.14 \cdot 25 \cdot 15 \] \[ = \frac{1}{3} \cdot 1177.5 \] \[ = 392.5 \text{ in}^3 \]
Summary of Calculated Volumes:
- 1570 cm³
- 424.57 in³
- 6.28 cm³
- 25.12 m³
- 392.5 in³
Please double-check your answers against these calculations. If you have the answers already, compare them to the ones provided above for accuracy.