We are given that a platform is in the shape of the following figure.
Note that the figure consists of two rectangular prisms and one cylinder. To find the volume of the figure, we need to find the volumes of the rectangular prisms and the cylinder. We will start with the upper rectangular prism. Recall that the volume of a rectangular prism with length l, width w, and height h can be calculated using the following formula.
V=l w hWe are given that l= 8, w= 20, and h= 5, so we have enough information to calculate the volume of the rectangular prism.
The volume of the upper rectangular prism is 800 m^3. Note that the lower rectangular prism has the same measures as the upper prism. Therefore, the volume of the lower rectangular prism is also 800 m^3. Next, we will find the volume of the cylinder. Let's 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
In this case, we are given the diameter and the height of the cylinder. To find the radius we can divide the diameter d by 2.
We got that the radius of the cylinder is 4 meters. Now, we can substitute the height and the radius into the formula and calculate the volume of the cylinder.
The volume of the cylinder is about 754 m^3. Finally, we can calculate the volume of the platform by adding the volumes that we found.
800+800+754=2354
Therefore, the volume of the platform is about 2354 m^3.
