Question
If the height of the cone is 5 cm and the volume is 500 cm^3, what is the radius of the cone?
(1 point)
Responses
The radius is the same as a cylinder with a volume of 500/3 and the same height.
The radius is the same as a cylinder with a volume of 500/3 and the same height.
The radius is the same as a cylinder with a volume 500(3) and same height.
The radius is the same as a cylinder with a volume 500(3) and same height.
The radius is the same as a cylinder with the same volume and height of 3.
The radius is the same as a cylinder with the same volume and height of 3.
The radius is the same as a cylinder with the same volume and same height.
(1 point)
Responses
The radius is the same as a cylinder with a volume of 500/3 and the same height.
The radius is the same as a cylinder with a volume of 500/3 and the same height.
The radius is the same as a cylinder with a volume 500(3) and same height.
The radius is the same as a cylinder with a volume 500(3) and same height.
The radius is the same as a cylinder with the same volume and height of 3.
The radius is the same as a cylinder with the same volume and height of 3.
The radius is the same as a cylinder with the same volume and same height.
Answers
GPT 3.5
The radius can be calculated using the formula for the volume of a cone, V = (1/3)πr^2h. Since the volume is 500 cm^3 and the height is 5 cm, we can plug in these values and solve for the radius:
500 = (1/3)πr^2(5)
1500 = πr^2(5)
1500 = 5πr^2
r^2 = 1500 / (5π)
r^2 = 300 / π
r ≈ √(300 / π)
r ≈ 8.66 cm (rounded to two decimal places)
Therefore, the radius of the cone is approximately 8.66 cm.
500 = (1/3)πr^2(5)
1500 = πr^2(5)
1500 = 5πr^2
r^2 = 1500 / (5π)
r^2 = 300 / π
r ≈ √(300 / π)
r ≈ 8.66 cm (rounded to two decimal places)
Therefore, the radius of the cone is approximately 8.66 cm.