A sphere and a right cylinder have the same radius and volume. the cylinder has a height of 3 inches find the radius.
4/3 * π * r^3 = π * r^2 * 3
4/3 * r = 3
To find the radius of the right cylinder, we need to use the given information that the sphere and the cylinder have the same radius and volume.
Let's start by finding the volume of the right cylinder. The formula for the volume of a cylinder is Vcylinder = π * r^2 * h, where r is the radius and h is the height.
Given:
Height of the cylinder, h = 3 inches
Volume of the cylinder, Vcylinder = Volume of the sphere
Now, let's find the volume of the sphere. The formula for the volume of a sphere is Vsphere = (4/3) * π * r^3, where r is the radius.
Given:
Volume of the sphere, Vsphere = Volume of the cylinder
Since the radius is the same for both the sphere and the cylinder, we can equate the volumes:
(4/3) * π * r^3 = π * r^2 * h
To simplify, we can cancel out π and r^2 on both sides:
(4/3) * r^3 = r^2 * h
Next, divide both sides of the equation by r^2:
(4/3) * r = h
Substitute the given height, h = 3 inches:
(4/3) * r = 3
Now, solve for r by multiplying both sides by 3/4:
r = (3 * 3/4) / (4/3)
r = (9/4) / (4/3)
r = (9/4) * (3/4)
r = 27/16
So, the radius of the right cylinder is 27/16 inches, or you can also express it as a decimal, approximately 1.6875 inches.