The volume of the pyramid and cone is one third the volume of the corresponding (ie same [size] base and height) prism and cylinder.
democritus calculated the volume of pyramids and cones
To find the volume of the cylinder ( V_1 ) that is not occupied by the cone, we first need to calculate the volumes of both the cone and the cylinder. The volume of the cone is given by ( V_{\text{cone}} = \frac{1}{3} \pi r^2 h ), while the volume of the cylinder is ( V_{\text{cylinder}} = \pi r^2 H ), where ( h ) is the height of the cone, ( H ) is the height of the cylinder, and ( r ) is the radius of the base. The volume of the space not occupied by the cone in the cylinder is then ( V_1 = V_{\text{cylinder}} - V_{\text{cone}} = \pi r^2 H - \frac{1}{3} \pi r^2 h ). Since the cone and the pyramid have the same volume, this relationship helps in understanding their dimensions but does not directly impact the volume calculation for the cylinder.
Volumes are cubic measures. Use a 3.
A meter is a measure of distance and cannot be a measure of volume. Therefore the question is incorrect in stating that the the numbers refer to volumes rather than lengths of edges, or it is incorrect in the units used for the volumes. Either of these errors make it impossible to answer the question in a sensible way.
The volume of a cone is 1/3 of the volume of a cylinder with the same radius and height
A cone is 1/3 of the volume of a cylinder with the same base and height. A pyramid is 1/3 of the volume of a prism with the same base and height.
democritus calculated the volume of pyramids and cones
The relationship between the formulas is that in all the radius is cubed.
you would use a graduated cylinder to measure volumes of liquids
Volumes are cubic measures. Use a 3.
A graduated cylinder measures the volume of liquids in milliliters or cubic centimeters. It is commonly used in laboratories for accurate measurement of liquid volumes.
A meter is a measure of distance and cannot be a measure of volume. Therefore the question is incorrect in stating that the the numbers refer to volumes rather than lengths of edges, or it is incorrect in the units used for the volumes. Either of these errors make it impossible to answer the question in a sensible way.
The volume of a cone is 1/3 of the volume of a cylinder with the same radius and height
The cone has 1/3 of the volume of the cylinder.
A graduated cylinder is used measuring precise volume of liquids.A graduated cylinder is used measuring precise volume of liquids.
A graduated cylinder measures volume of liquids or other substances in milliliters or liters.
It isn't. If the cylinder and the cone have the same height and radius, the cylinder has a larger volume (twice as large). If they do not have the same height and radius you need more information to prove their relative volumes.