Write the formulas to find the volume of the solids involved. Then, find the corresponding ratio.
Ratio: 23 Description: The volume of the sphere is two thirds the volume of the cylinder.
Practice makes perfect
Let's begin by writing the formulas to find the volume of a sphere and a cylinder.
Volume Formulas
Sphere
Cylinder
V_s = 4Ï€ r^3/3
V_c = π r^2h
Let's assume that both solids have the same radius and that h=2r. Let's calculate the volume of the cylinder with this height.
V_c = π r^2(2r)
⇒
V_c = 2 π r^3
Next, let's simplify the ratio of the volume of the sphere to the volume of the cylinder, V_sV_c.
The volumes are in a ratio of 2:3. This implies that the volume of the sphere is two thirds the volume of the cylinder.
Extra
Example
Let's consider a spherical water tank with radius r. The amount of water needed to fill this tank can fill only 2/3 of a cylindrical tank with the same radius and height equal to 2r.
