How would changing the dimensions affect the volume of the cone? Give specific examples.
Changing the dimensions of a cone would directly affect its volume because volume is dependent on the dimensions of the shape.
For example:
1. If the height of the cone is increased while the radius remains the same, the volume of the cone would increase because the cone's shape would become taller and therefore hold more space.
2. If the radius of the cone is increased while the height remains the same, the volume of the cone would also increase because the base of the cone would be larger, allowing it to hold more volume.
3. If both the height and radius are decreased, the volume of the cone would decrease because the cone's overall size would be smaller, resulting in less space being held within the cone.
In general, increasing the dimensions of the cone would increase its volume, while decreasing the dimensions would decrease the volume.