Question

The volume of a cone is 25/3 * pi*c * m ^ 3 What is the volume of a sphere if its radius is the same as the cone's and the height of the cone is equal to the sphere's diameter? (1 point)
25/6 * pi*c * m ^ 3;
25/2 * pi*c * m ^ 3;
25pi*c * m ^ 3;
50/3 * pi*c * m ^ 3

Answer 1

That’s not a answer

Answer 2

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

Since the radius of the sphere is the same as the cone's, we can say that r = m.

The height of the cone is equal to the sphere's diameter, which means h = 2r = 2m.

Now, let's substitute these values into the formula for the volume of the cone:

V_cone = (25/3) * pi * c * m^3

Since the height of the cone is equal to 2r, we can rewrite the formula as:

V_cone = (25/3) * pi * c * (h/2)^3

Simplifying further:

V_cone = (25/3) * pi * c * (1/8) * h^3

Now, we can substitute this into the formula for the volume of the sphere:

V_sphere = (4/3) * pi * r^3

V_sphere = (4/3) * pi * (m^3)

Since the cone's volume is equal to the sphere's volume, we can set these two equations equal to each other:

(25/3) * pi * c * (1/8) * h^3 = (4/3) * pi * (m^3)

Simplifying further:

(25/3) * (1/8) * h^3 = (4/3) * (m^3)

(25/24) * h^3 = (4/3) * (m^3)

Multiplying both sides by (24/25):

h^3 = (4/3) * (m^3) * (24/25)

h^3 = (96/75) * (m^3)

h^3 = (32/25) * (m^3)

Taking the cube root of both sides:

h = (32/25)^(1/3) * (m)

So, the formula for the volume of the sphere with the given conditions is:

V_sphere = (4/3) * pi * (m^3) = (4/3) * pi * [(32/25)^(1/3) * (m)]^3 = (4/3) * pi * (32/25) * (m^3)

Simplifying:

V_sphere = (32/25) * (4/3) * pi * (m^3) = (32/25) * (4/3) * pi * (m^3) = (128/75) * pi * (m^3)

Thus, the correct answer is 128/75 * pi * c * m^3.

Answer 3

Apologies for the confusion. Let's go through the problem again.

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

Given that the volume of the cone is (25/3) * pi * c * m^3, we can set up the equation as:

(25/3) * pi * c * m^3 = (1/3) * pi * r^2 * h

Since the radius of the cone is equal to the radius of the sphere, we can say that r = m.

And since the height of the cone is equal to the diameter of the sphere, we can say that h = 2r = 2m.

Substituting these values into the equation, we get:

(25/3) * pi * c * m^3 = (1/3) * pi * m^2 * (2m)

Simplifying:

(25/3) * pi * c * m^3 = (1/3) * pi * 2m^3

Cross-multiplying, we get:

(25/3) * c * m^3 = (2/3) * m^3

Dividing both sides by (2/3) * m^3, we get:

(25/3) * c = 1

Simplifying further:

25c = 3

Dividing both sides by 25, we get:

c = 3/25

Now, we can substitute this value back into the volume of the cone equation to find the volume of the sphere:

V_sphere = (4/3) * pi * r^3

V_sphere = (4/3) * pi * (m^3)

V_sphere = (4/3) * pi * [(2/3) * m^3]

V_sphere = (8/9) * pi * m^3

So the answer is (8/9) * pi * m^3.