Question
write it out simple and short. What is the formula for the volume of a cylinder with radius r and height h? In 3–5 sentences, describe an informal argument for this volume formula.(4 points)
Answers
GPT-4o mini
The formula for the volume of a cylinder with radius \( r \) and height \( h \) is \( V = \pi r^2 h \).
To understand this, imagine the cylinder as a series of circular slices stacked on top of each other, each with a radius \( r \). The area of one circular slice is \( \pi r^2 \). Since there are \( h \) of these slices (one for each unit of height), you multiply the area of the base by the height to get the total volume: \( \text{Base Area} \times \text{Height} = \pi r^2 \times h \). Thus, the volume of the cylinder is \( V = \pi r^2 h \).
To understand this, imagine the cylinder as a series of circular slices stacked on top of each other, each with a radius \( r \). The area of one circular slice is \( \pi r^2 \). Since there are \( h \) of these slices (one for each unit of height), you multiply the area of the base by the height to get the total volume: \( \text{Base Area} \times \text{Height} = \pi r^2 \times h \). Thus, the volume of the cylinder is \( V = \pi r^2 h \).