A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 3 inches. Find the radius.
Vs = (4/3) pi r^3
Vc = pi r^2 h where h = 3
so
4/3 pi r^3 = pi r^2 h
4 r^3 = 3 r^2 * 3
r = (9/4)
To find the radius of the right cylinder, we need to first determine the volume of both the sphere and the cylinder using the given information.
The volume of a sphere is given by the formula: V_sphere = (4/3) * π * r^3, where 'r' represents the radius of the sphere.
The volume of a right cylinder is given by the formula: V_cylinder = π * r^2 * h, where 'r' represents the radius of the cylinder and 'h' represents the height.
Since we know that the volume of the sphere and the cylinder are equal, we can set up an equation:
(4/3) * π * r^3 = π * r^2 * 3
To solve for the radius, we can cancel out the common factor of π and divide both sides of the equation by 3:
(4/3) * r^3 = r^2
Now, we can solve for the radius 'r'. Multiply both sides of the equation by 3/4 to isolate 'r':
r^3 = (3/4) * r^2
Divide both sides of the equation by 'r^2' to get:
r = 3/4
Hence, the radius of the right cylinder is 3/4 inches.
cylinder volume = sphere volume ... π r^2 h = 4/3 π r^3
dividing by (π r^2) ... h = 4/3 r