Volume of a sphere is 60 cubic meters. Find volume of cylinder with same dimensions.
To find the volume of a cylinder with the same dimensions as a sphere, we first need to find the radius of the sphere.
The formula for the volume of a sphere is:
V = (4/3)πr³
Where V is the volume and r is the radius.
Since the volume of the sphere is given as 60 cubic meters, we can set up the equation:
60 = (4/3)πr³
To find the radius, we need to isolate r. Divide both sides of the equation by (4/3)π:
60 / ((4/3)π) = r³
Rearrange the equation to solve for r:
r³ = (60 / ((4/3)π))
r³ = (60 / (4/3)) * (3/π)
r³ = (60 * 3) / (4 * π)
r³ = 180 / (4 * π)
r³ = 45 / π
Now we can find the volume of the cylinder. The formula for the volume of a cylinder is:
V = πr²h
Where V is the volume, r is the radius, and h is the height.
Since the height is not given, we can make assumptions about the height of the cylinder to find its volume relative to that of the sphere. Let's assume the height of the cylinder is equal to the diameter of the sphere. The diameter is calculated as twice the radius:
d = 2r
Now we can find the volume of the cylinder:
V_cylinder = πr²h
V_cylinder = πr²(2r)
V_cylinder = 2πr³
Substituting the value of r³ we found earlier:
V_cylinder = 2π * (45 / π)
Simplifying the equation:
V_cylinder = 90 cubic meters
Therefore, the volume of the cylinder with the same dimensions as the sphere is 90 cubic meters.