What is the volume of a cone with a diameter of 20cm and a height of 15 cm
To calculate the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Where \( V \) is the volume, \( r \) is the radius of the base, \( h \) is the height, and \( \pi \) is a mathematical constant approximately equal to 3.14159.
First, you need to find the radius of the cone. The radius is half the diameter, so if the diameter is 20 cm, the radius \( r \) is:
\[ r = \frac{d}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm} \]
Now, insert the radius and height into the formula:
\[ V = \frac{1}{3} \pi (10 \text{ cm})^2 \times 15 \text{ cm} \]
\[ V = \frac{1}{3} \pi \times 100 \text{ cm}^2 \times 15 \text{ cm} \]
\[ V = \frac{1}{3} \pi \times 1500 \text{ cm}^3 \]
\[ V = 500 \pi \text{ cm}^3 \]
Now you can multiply by \( \pi \):
\[ V \approx 500 \times 3.14159 \]
\[ V \approx 1570.795 \text{ cm}^3 \]
So the volume of the cone is approximately 1570.795 cubic centimeters (cm³).