Question

to calculate the volume of a cone, you need the radius of the base and the of the cone. in experiments, filling a cone with the same base and height as a cylinder shows that it takes cones to fill one cylinder. a is a three - dimensional shape with a circular base and a single vertex.

Explanation:

1. The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height of the cone. So, to calculate the volume of a cone, you need the radius of the base and the height of the cone.
2. The volume of a cylinder with radius \(r\) and height \(h\) is \(V_{cylinder}=\pi r^{2}h\), and the volume of a cone with the same radius \(r\) and height \(h\) is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). If we let \(n\) be the number of cones needed to fill the cylinder, then \(n\times V_{cone}=V_{cylinder}\). Substituting the formulas, we have \(n\times\frac{1}{3}\pi r^{2}h=\pi r^{2}h\). Solving for \(n\), we get \(n = 3\). So, it takes 3 cones to fill one cylinder.
3. By the definition of a cone, a cone is a three - dimensional shape with a circular base and a single vertex.

Answer:

1. height
2. 3
3. cone