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.
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
1 answer
1 answer