Note that the solid consists of a hemisphere and a cylinder. To find the volume of the solid, we need to find the volumes of the hemisphere and the cylinder. We will start with the hemisphere. Recall that the volume of a hemisphere with radius r is half the volume of a sphere with radius r.
Volume of a Hemisphere [0.8em]
V=1/2(4/3π r^3) ⇔ V=2/3π r^3In this case, the radius of the hemisphere is 3 inches. We can substitute the radius into the formula and calculate the volume of the hemisphere.
The volume of the hemisphere is about 56.549 cubic inches. Next, we will find the volume of the cylinder. We will start by recalling that the volume of a cylinder with the radius r and height h can be calculated by the following formula.
V=Ï€ r^2 h
The given cylinder has a height of 2 inches and a radius of 3 inches. Let's substitute these values into the formula and calculate the volume of the cylinder.
The volume of the cylinder is about 56.549 cubic inches. Finally, we can calculate the volume of the solid by adding the volumes that we found.
56.549+56.549=113.098 ≈ 113.1
Therefore, the volume of the solid is about 113.1 cubic inches.
