H. How is the formula for the volume of a cylinder like the formula for the volume of a prism? Why does this make sense? Hint: Think about how cylinders are like prisms.
The formula for the volume of a cylinder is V = πr^2h, while the formula for the volume of a prism is V = Bh, where B is the area of the base and h is the height. These formulas are similar because a cylinder can be thought of as a prism with a circular base. The circular base of the cylinder has an area of πr^2, which is the same as the area of a circle with radius r. So, the formula for the volume of a cylinder includes πr^2 as the base area, just like the formula for the volume of a prism includes B as the base area. This makes sense because both shapes have a base and a height, and the volume of each can be calculated by multiplying the base area by the height.
