We want to decide which of the two solids has a greater volume: a cylinder with base's radius of 38 units and height of 71 units or a rectangular prism with dimensions, or a rectangular prism with dimensions 34, 84, and 99 units. To do so, let's first recall the formula for the volume V of a cylinder.
V = π r^2 h
Here, r is the radius of a cylinder's base and h is the cylinder's height. In our case, r= 38 and h= 71. Let's substitute these values into our formula and find the volume.
The cylinder's volume is about 322 088.6 cubic units. Now, let's recall the formula for the volume V of a rectangular prism.
V = l w h
Here l is the prism's length, w is its width, and h is its height. In our case, the prism has dimensions 34, 84, and 99 units, so we can treat 34 as the length, 84 as the width, and 99 as the height. Let's substitute these values and find the volume.
The prism has a volume of 282 744 cubic units. This is less than the cylinder's volume of about 322 088.6 cubic units. Therefore, the cylinder has a greater volume.
