The volume of a sphere is 72m3. What is the volume of a cone if its radius is the same as the sphere's and its height is equal to the sphere's diameter?

Answer 1

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.

Given that the volume of the sphere is 72m^3, we can equate the formula to 72 and solve for the radius.

72 = (4/3)πr^3
72 * 3/4π = r^3
54π = r^3
r = (54π)^(1/3)

Since the radius of the sphere is the same as the radius of the cone, we can substitute the radius into the volume formula for a cone.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.

For the cone, the height is equal to the sphere's diameter, which is 2 times the radius.
h = 2r

Substituting the radius and height into the formula, we get:

V = (1/3)π((54π)^(1/3))^2(2((54π)^(1/3)))
= (1/3)π(54π)^(2/3)(2(54π)^(1/3))
= 108π(54π)^(1/3)

So, the volume of the cone with the given conditions is 108π(54π)^(1/3) cubic meters.

Answer 2

it says its wrong bot

Answer 3

I apologize for the incorrect response.

Let's try again to find the volume of the cone.

Given that the volume of the sphere is 72m^3, we can equate the formula to 72 and solve for the radius.

72 = (4/3)πr^3
r^3 = (3/4π)(72)
r^3 = 27π
r = (27π)^(1/3)

Since the radius of the sphere is the same as the radius of the cone, we can substitute the radius into the volume formula for a cone.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.

For the cone, the height is equal to the sphere's diameter, which is 2 times the radius.
h = 2r

Substituting the radius into the volume formula for the cone:

V = (1/3)π((27π)^(1/3))^2(2((27π)^(1/3)))
= (1/3)π(27π)^(2/3)(2(27π)^(1/3))
= (1/3)π(27π)(2)(27)^(1/3)
= 18π(27)^(1/3)

So, the volume of the cone with the given conditions is 18π(27)^(1/3) cubic meters.