What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? (1 point) Responses 6,280 cubic centimeters 6,280 cubic centimeters 314 cubic centimeters 314 cubic centimeters 2,355 cubic centimeters 2,355 cubic centimeters 1,570 cubic centimeters
First, we should find the radius of the cone. The radius is half the diameter:
\( r = \frac{d}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm} \)
The formula for the volume of a cone is:
\( V = \frac{1}{3} \pi r^2 h \)
where \( V \) is the volume, \( \pi \) is approximately 3.14159, \( r \) is the radius and \( h \) is the height.
Plugging in the values for \( r \) and \( h \):
\( V = \frac{1}{3} \pi (10 \text{ cm})^2 \times 15 \text{ cm} \)
\( V = \frac{1}{3} \pi \times 100 \text{ cm}^2 \times 15 \text{ cm} \)
\( V = \frac{1}{3} \pi \times 1500 \text{ cm}^3 \)
\( V = 500 \pi \text{ cm}^3 \)
\( V = 500 \times 3.14159 \text{ cm}^3 \)
\( V \approx 1570.795 \text{ cm}^3 \)
Rounding to everyday use, the volume is approximately 1,570 cubic centimeters. So, the last option you've provided, "1,570 cubic centimeters," is the correct answer.