What type of solid is represented by the formula V = πr²h?

What type of solid is represented by the formula V = πr²h?

• A. Cube
• B. Cylinder
• C. Sphere
• D. Pyramid

Answer: (B)

The formula \( V = \pi r^2 h \) is specifically used to calculate the volume of a cylinder. In this formula, \( r \) represents the radius of the circular base of the cylinder, and \( h \) is the height of the cylinder. To derive this formula intuitively, the area of the base of the cylinder is calculated using \( \pi r^2 \), which gives the area of a circle. Since the cylinder extends vertically to a height \( h \), the volume is determined by multiplying this area by the height, effectively stacking the circular base \( h \) times to create the three-dimensional shape of the cylinder. This is why the correct answer is the cylinder, as it accurately matches the geometric properties expressed in the volume formula provided in the question.

The formula ( V = \pi r^2 h ) is specifically used to calculate the volume of a cylinder. In this formula, ( r ) represents the radius of the circular base of the cylinder, and ( h ) is the height of the cylinder.

To derive this formula intuitively, the area of the base of the cylinder is calculated using ( \pi r^2 ), which gives the area of a circle. Since the cylinder extends vertically to a height ( h ), the volume is determined by multiplying this area by the height, effectively stacking the circular base ( h ) times to create the three-dimensional shape of the cylinder.

This is why the correct answer is the cylinder, as it accurately matches the geometric properties expressed in the volume formula provided in the question.