Sphere: V = 43π r^3 Cylinder: S.A. =2π r^2+2π rh Hemisphere: V = 23π r^3 Cone: S.A. = π r l + π r^2
Practice makes perfect
We are asked to match each figure with its correct volume or surface area formula. Before we do that, we should identify each figure. Let's do it one by one.
Sphere
In the graph we can see that the first solid is a sphere. We are told that the radius of the sphere equals 2 feet.
Only one of these expressions appears in the right column — the formula for the volume of a sphere. This means we can connect the sphere with the formula for the volume.
Cylinder
The second solid is a cylinder. We know this because it has parallel bases that are circles.
The second formula, the formula for the surface area of a cylinder, appears in the right column. We can match the cylinder with this formula.
Hemisphere
The third figure is a half of a sphere. This makes it a hemisphere.
The volume and the surface area of a hemisphere are strictly related to the volume and surface area of a sphere. The volume is exactly half the volume of a sphere. The surface area is half the surface area of a sphere plus the area of the circular base.
Volume
Surface Area
V = 1/2(4/3Ď€ r^3) or 2/3Ď€ r^3
S.A. = 1/2(4Ď€ r^2) or 2Ď€ r^2
See that the formula for the volume matches the last one shown in the exercise.
Cone
The last figure is a cone. The diameter of the base of the cone is 10 inches and the height is 9 inches.
We should match the cone with the correct formula for its volume or surface area.
Let's remember these formulas then. Here are the formulas for the volume and the surface area of a cone with a radius r, height h, and slant height l.
Volume
Surface Area
V = 1/3Ď€ r^2h
S.A. = π r l + π r^2
See that the formula for the surface area is the second one of the listed formulas. We can match it with the figure.
