Question
Which option best describes an informal argument for why the volume of a cylinder of radius r and height h is V=πr2h ?(1 point) Responses A cylinder is a stack of r circles, each with a thickness of one unit and an area of πrh . A cylinder is a stack of r circles, each with a thickness of one unit and an area of πrh . A cylinder is a stack of r circles, each with a thickness of one unit and an area of πr2 . A cylinder is a stack of r circles, each with a thickness of one unit and an area of πr2 . A cylinder is a stack of h squares, each with a thickness of one unit and an area of πr2 . A cylinder is a stack of h squares, each with a thickness of one unit and an area of πr2 . A cylinder is a stack of r squares, each with a thickness of one unit and an area of πrh .
Answers
GPT-4o mini
The best option that describes an informal argument for why the volume of a cylinder of radius \( r \) and height \( h \) is \( V = \pi r^2 h \) is:
**A cylinder is a stack of \( h \) circles, each with a thickness of one unit and an area of \( \pi r^2 \).**
This option correctly identifies that the volume of the cylinder can be understood as the area of the base (which is a circle with area \( \pi r^2 \)) multiplied by the height \( h \), resulting in \( V = \pi r^2 h \).
**A cylinder is a stack of \( h \) circles, each with a thickness of one unit and an area of \( \pi r^2 \).**
This option correctly identifies that the volume of the cylinder can be understood as the area of the base (which is a circle with area \( \pi r^2 \)) multiplied by the height \( h \), resulting in \( V = \pi r^2 h \).