What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? (1 point) 2,355 cubic centimeters 6,280 cubic centimeters 314 cubic centimeters 1,570 cubic centimeters
The volume of a cone is given by the formula:
\[ \text{Volume} = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base of the cone and \( h \) is the height of the cone.
Given that the diameter of the cone is 20 cm, the radius \( r \) is half of that, so:
\[ r = \frac{20}{2} = 10 \text{ cm} \]
And given the height \( h \) is 15 cm, we can now plug the values into the volume formula:
\[ \text{Volume} = \frac{1}{3} \pi (10)^2 (15) \]
\[ \text{Volume} = \frac{1}{3} \pi (100) (15) \]
\[ \text{Volume} = \frac{1}{3} (1500 \pi) \]
\[ \text{Volume} = 500 \pi \]
Now, using the approximation \( \pi ≈ 3.14159 \), we calculate:
\[ \text{Volume} ≈ 500 \times 3.14159 \]
\[ \text{Volume} ≈ 1570.795 \text{ cubic centimeters} \]
Rounded to the nearest whole number, the volume of the cone is approximately 1,571 cubic centimeters. Therefore, the closest answer from the given options is:
1,570 cubic centimeters.