The volume of a sphere is 48m³ what is the volume of a cylinder if it's radius is the same ad the spheres and its height is equal to the spheres diameter??
To find the volume of the cylinder, we need to know the radius of the sphere. Since the radius of both the sphere and the cylinder is the same, we can determine the radius of the sphere by using the volume formula:
Volume of a sphere = (4/3)πr³
48m³ = (4/3)πr³
To solve for r, we multiply both sides of the equation by (3/4) and divide both sides by π:
r³ = (48m³ * (3/4)) / π
r³ = 36m³ / π
r = (∛(36m³ / π))
Once we find the radius, we can use it to calculate the volume of the cylinder. Note that the height of the cylinder is equal to the diameter of the sphere, which means it is twice the radius.
Height of the cylinder = 2r
Therefore, the volume of the cylinder is given by:
Volume of the cylinder = πr² * height
Volume of the cylinder = π * (∛(36m³ / π))² * (2 * ∛(36m³ / π))
What was it?
I apologize for the confusion in my previous response. Let's calculate the volume of the cylinder with the given information.
We know that the volume of the sphere is 48m³, and the radius of the sphere and the cylinder are the same. Let's assume the radius of the sphere and cylinder is denoted as "r".
Given that the volume of a sphere is given by the formula:
Volume of a sphere = (4/3)πr³
We can rearrange the equation to solve for the radius:
r = ∛((3/4)*(48m³)/π)
By calculating this, we find that the radius "r" is equal to the cube root of (36m³/π).
Now, the height of the cylinder is given as the diameter of the sphere. Since the diameter is twice the radius, the height of the cylinder is:
Height of the cylinder = 2r
Plugging in the value of the radius, the height of the cylinder is:
Height of the cylinder = 2 * ∛(36m³/π)
Finally, to calculate the volume of the cylinder, we use the formula:
Volume of the cylinder = π * r² * height
Plugging in the values of the radius and height, the volume of the cylinder is:
Volume of the cylinder = π * (∛(36m³/π))² * (2 * ∛(36m³/π))