Note that the solid consists of a hemisphere and a cone. To find the volume of the solid, we need to find the volumes of the hemisphere and the cone. 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, we are given the diameter of the hemisphere. To find the radius, we need to divide the diameter d by 2. Let's do it!
The volume of the hemisphere is about 718.4 cm^3. Next, we will find the volume of the cone. We will start by recalling that the volume of a cone with the radius r and height h can be calculated by the following formula.
V=1/3Ï€ r^2 h
The given cone has a height of 11 centimeters. Note that the diameter of the cone is equal to the diameter of the hemisphere. Therefore, these solids have also the same radius. This means that the radius of the cone is 7 centimeters. Let's substitute the height and the radius into the formula and calculate the volume of the cone.
The volume of the cone is about 564.4 cm^3. Finally, we can calculate the volume of the solid by adding the volumes that we found.
718.4+564.4= 1282.8
Therefore, the volume of the solid is about 1282.8 cm^3.
