The volume of a cone is 25/3 pi centimeters, cubed. What is the volume of a sphere if it’s radius is the same as the cones and the height of the cone is equal to the spheres diameter?
50/3 pi centimeters, cubed
25/6 pi centimeters cubed
25 pi cm³
25/2, pi cm³
We know that the volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height. In this case, the volume of the cone is given as (25/3)π cm³.
The height of the cone is equal to the diameter of the sphere, which means the height is 2r (twice the radius).
Substituting this value into the volume formula, we get (25/3)π = (1/3) * π * r^2 * (2r).
Now, canceling out π and multiplying both sides by 3 gives 25 = 2r^3.
Dividing by 2 gives r^3 = 12.5, and taking the cube root of both sides gives r ≈ 2.714.
The volume of a sphere is given by the formula V = (4/3) * π * r^3. Substituting the value of r from above into this formula, we get V = (4/3) * π * (2.714)^3.
Evaluating this expression gives V ≈ 50.95 cm³, which is approximately equal to 50/3 π cm³.
Therefore, the volume of the sphere is approximately 50/3 π cm³.