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
1,570 cubic centimeters
1,570 cubic centimeters
2,355 cubic centimeters
2,355 cubic centimeters
To find the volume of a cone, you can use the following formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base of the cone, \( h \) is the height, and \( \pi \) is approximately 3.14159.
Given that the diameter of the cone is 20 cm, the radius \( r \) will be half of the diameter, which is \( r = 20\, \text{cm} / 2 = 10\, \text{cm} \).
The height \( h \) of the cone is given as 15 cm.
Plugging in the numbers:
\[ V = \frac{1}{3} \pi (10\, \text{cm})^2 \times 15\, \text{cm} \]
\[ V = \frac{1}{3} \pi \times 100\, \text{cm}^2 \times 15\, \text{cm} \]
\[ V = \frac{1}{3} \times 3.14159 \times 1500\, \text{cm}^3 \]
\[ V = 1570.795 \text{cm}^3 \]
Rounding to the nearest cubic centimeter, the volume of the cone is approximately 1,571 cubic centimeters.
Therefore, the correct answer is:
1,570 cubic centimeters