A sphere of radius 3 is inscribed in a cylinder. What is the volume inside the cylinder but not inside the sphere?
well, the radius of the cylinder is 3, and its height is the diameter of the sphere = 6
you want the volume of the cylinder minus that of the sphere:
pi r^2 h - 4/3 pi r^3
To find the volume inside the cylinder but not inside the sphere, we need to find the volume of the cylinder and subtract the volume of the sphere.
First, let's find the volume of the cylinder. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is the height. In this case, the radius of the cylinder is also 3.
Next, let's find the volume of the sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius of the sphere is also 3.
Now, let's calculate the volume of the cylinder using the formula V = πr^2h. With the radius of the cylinder being 3, we have V_cylinder = π(3^2)h.
Let's calculate the volume of the sphere using the formula V = (4/3)πr^3. With the radius of the sphere being 3, we have V_sphere = (4/3)π(3^3).
Finally, calculating the volume inside the cylinder but not inside the sphere can be done by subtracting the volume of the sphere from the volume of the cylinder: V_inside_cylinder = V_cylinder - V_sphere.
Substituting the calculated values, we have V_inside_cylinder = π(3^2)h - (4/3)π(3^3).
Simplifying further, V_inside_cylinder = π(9h - 36).
So, the volume inside the cylinder but not inside the sphere is π(9h - 36).