The composite solid is formed by a hemisphere and a cylinder. To find the volume, remember that the volume of a composite solid is either the sum or difference between the volumes of the individual solids. Let's do one at time!
Volume of Hemisphere
Recall the formula for the volume of a hemisphere.
V_h= 1/2* 4/3Ï€ r^3
Here, r represent the radius of the hemisphere. In our case, the diameter of the hemisphere is equal to 6 inches, then the radius of the hemisphere is 3 inches. We can substitute this value into the above formula to calculate the volume of the hemisphere.
The volume of the hemisphere is about 56.5 cubic inches.
Volume of Cylinder
Now, let's recall the formula for the volume of a cylinder.
V_c=Bh
Here, B represents the area of the base and h is the height of the cylinder. The base is a circle, so we can find the area by recalling the area of a circle with radius r.
B=Ï€ r^2
In our case, the diameter is 6 inches which means that the radius is 3 feet. Then, we can calculate the base area of the cylinder by substituting r= 3 into the above formula.
The volume of the cylinder is about 311 cubic inches. Now that we have the volume of each solid, we can subtract them to find the volume of the composite solid.
V= V_c - V_h → V≈ 254.5 in^3
