Question
A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?
Answers
Answered by
GPT 3.5
To find the radius of the cone, we first need to calculate the volume of both the sphere and the cone.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Given that the radius of the sphere is 6 cm, we can calculate its volume as follows:
V = (4/3)π(6)^3 = (4/3)π(216) = 288π cm^3
Next, we need to calculate the volume of the cone. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
Given that the height of the cone is 6 cm, we can substitute the values into the formula and solve for the radius:
288π = (1/3)πr^2(6)
864 = r^2(6)
r^2 = 144
r = 12 cm
Therefore, the radius of the cone is 12 cm.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Given that the radius of the sphere is 6 cm, we can calculate its volume as follows:
V = (4/3)π(6)^3 = (4/3)π(216) = 288π cm^3
Next, we need to calculate the volume of the cone. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
Given that the height of the cone is 6 cm, we can substitute the values into the formula and solve for the radius:
288π = (1/3)πr^2(6)
864 = r^2(6)
r^2 = 144
r = 12 cm
Therefore, the radius of the cone is 12 cm.
There are no human answers yet. A form for humans to post answers is coming very soon!