To solve this problem, we need to use the relationship between the volumes of a cylinder, cone, and sphere:
1. Volume of a cylinder: V_cylinder = π * r^2 * h
2. Volume of a cone: V_cone = (1/3) * π * r^2 * h
3. Volume of a sphere: V_sphere = (4/3) * π * r^3
Given that the volume of the cylinder is 36 cm^3, we can substitute the values into the cylinder volume formula:
36 = π * r^2 * h
We then know that the height of the cylinder is equal to the sphere's diameter, so h = 2r.
Substituting this into the equation, we have:
36 = π * r^2 * 2r
Simplifying further:
36 = 2π * r^3
Dividing both sides of the equation by 2π:
r^3 = 18/π
Now we can find the volume of the sphere using the sphere volume formula:
V_sphere = (4/3) * π * r^3
Substituting the value of r^3 we found:
V_sphere = (4/3) * π * (18/π)
Simplifying:
V_sphere = 4 * r^3
Therefore, the volume of the sphere is 4 * (18/π) cm^3.
using the relationship among the formulas for the volumes of cones cylinders and spheres to solve the following problem the volume of a cylinder is 36 sm^3 what is the volume of a sphere if its radius is the same as the cylinder's and the height of the cylinder is equal to the sphere's diameter
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