Question

The volume of a cone is 72 cm^3. What is the volume of a cone if its radius is the same as the sphere's and its height is equal to the spheres diameter?
_ cm^3

Answer 1

Thats wrong

Answer 2

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

Given that the volume of the cone is 72 cm^3, we can set up the equation as follows:

72 = (1/3)πr^2h

Since the radius of the cone is the same as the sphere's, and the height is equal to the sphere's diameter (which is twice the radius of the sphere), we can substitute r for the radius of the sphere and h for 2r:

72 = (1/3)π(r^2)(2r)

72 = (2/3)πr^3

Solving for r:

r^3 = 36/π

r ≈ 3.097 cm

Now we can substitute this value of r back into the formula for the volume of a cone:

V = (1/3)π(3.097)^2(2(3.097))
V ≈ 57.73 cm^3

Therefore, the volume of the cone with a radius equal to the sphere's and a height equal to the sphere's diameter is approximately 57.73 cm^3.

Answer 3

My apologies for the mistake. Let's re-calculate:

Given the volume of the cone is 72 cm^3, we can use the formula for the volume of a cone: V = (1/3)πr^2h.

Since the radius of the cone is the same as the sphere's, and the height of the cone is equal to the sphere's diameter, the height of the cone (h) is twice the radius of the sphere.

Let's set the height of the cone as h = 2r, where r is the radius.

The volume of the cone, given as 72 cm^3, can be written as:

72 = (1/3)πr^2(2r)
72 = (2/3)πr^3

Solving for r:

r^3 = 36 / (2π)
r = (36 / (2π))^(1/3)
r ≈ 2.532 cm

Now, substitute this value back into the formula for the volume of the cone:

V = (1/3)π(2.532)^2(2 * 2.532)
V ≈ 42.757 cm^3

Therefore, the volume of the cone, when the radius is the same as the sphere's and the height is equal to the sphere's diameter, is approximately 42.757 cm^3.