Question

The volume of a cone is 25/3 cm 3. What is the volume of a sphere that if it’s radius is the same as the cones and the height of the cone is equal to the spheres diameter?

Answer 1

To find the volume of a sphere, we need to know its radius (r). We are given that the radius of the sphere is the same as the radius of the cone.

We are also given that the height of the cone is equal to the diameter of the sphere. Let's first find the height of the cone.

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

We are given that V (volume of the cone) = 25/3 cm^3.
We are also given that the radius (r) of the cone is the same as the radius of the sphere.

Therefore, we can write the equation as: 25/3 = (1/3)πr^2h.

We know that the height (h) of the cone is equal to the diameter of the sphere, which is 2r.

Substituting h = 2r in the equation, we get: 25/3 = (1/3)πr^2(2r).

Simplifying further, we have: 25/3 = (2/3)(πr^3).

Multiplying both sides by 3/2 to isolate r^3 on the right side, we get: r^3 = (25/3) * (3/2).

Simplifying further, we have: r^3 = 25/2.

Now we can find r by taking the cube root of both sides: r = ∛(25/2).

Once we have the value of r, we can find the volume of the sphere using the formula: V_sphere = (4/3)πr^3.

Calculating the volume of the sphere, we have: V_sphere = (4/3)π(∛(25/2))^3.

Simplifying, we find: V_sphere ≈ 65.45 cm^3.

Therefore, the volume of the sphere is approximately 65.45 cm^3.