Changing the dimensions of a cone, specifically the height and radius, will affect the volume of the cone.
1. Increasing the height: If the height of the cone is increased, the volume of the cone will also increase. This is because the volume of a cone is directly proportional to the height. For example, if the height of a cone is doubled while the radius remains the same, the volume of the cone will increase by a factor of 2.
2. Increasing the radius: If the radius of the cone is increased, the volume of the cone will also increase. This is because the volume of a cone is directly proportional to the square of the radius. For example, if the radius of a cone is doubled while the height remains the same, the volume of the cone will increase by a factor of 4.
3. Decreasing the height or radius: Conversely, if the height or radius of the cone is decreased, the volume of the cone will decrease. This is because the volume of a cone is directly proportional to the height and the square of the radius. For example, if the height of a cone is halved while the radius remains the same, the volume of the cone will decrease by a factor of 2.
How would changing the dimensions affect the volume of the cone? Give specific examples.
1 answer