Question

the process of deriving the formula for the volume of a cone is based on comparing its volume to that of a with the same dimensions. 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:

• For the first blank, the formula for the volume of a cone \( V=\frac{1}{3}\pi r^{2}h \) is derived by comparing it to a cylinder with the same \( r \) (radius) and \( h \) (height) since \( V_{cylinder}=\pi r^{2}h \).
• For the second blank, the volume formula \( V = \frac{1}{3}\pi r^{2}h \) requires the radius of the base (\( r \)) and the height (\( h \)) of the cone.
• For the third blank, from the volume relationship \( V_{cylinder}=3V_{cone}\) (when \( r\) and \( h\) are equal), it takes \( 3 \) cones to fill one cylinder.
• For the fourth blank, the geometric shape described with a circular base and a single vertex is a cone.

Answer:

1. cylinder
2. height
3. \( 3 \)
4. cone