The composite solid is formed by a hemisphere and a cube. 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* 4/3π r^3
Here, r represent the radius of the hemisphere. In our case, the diameter of the hemisphere is equal to the side length of the square. Since the side length is equal to 8 centimeters, then the radius of the hemisphere is equal to 4 centimeters. We can substitute this value into the above formula to calculate the volume of the hemisphere.
The volume of the hemisphere is about 134.04 cubic centimeters.
Volume of Cube
Now, we will use the formula for the volume of a cube.
V_c=s^3
Here, s represents the side length of the cube. We know that the side length of the cube is equal to 8 centimeters. Let's substitute s= 8 into the above formula to find the volume.
The volume of the cube is 512 cubic centimeters. Now that we have the volume of each solid, we can add them to find the volume of the composite solid.
V= V_h + V_c → V= 646.04 cm^3
