Finding Missing Dimensions in Geometry Practice

Volume of 3D Shapes

• The volume of a cylinder can be found by calculating the area of its base (πr^2) and multiplying it by its height (h).

Spheres

• A sphere with a volume of 4,500π cubic inches has a radius that can be found by rearranging the formula for the volume of a sphere (V = (4/3)πr^3).
• A unit sphere is not a good unit of volume measurement for all spheres because spheres come in different sizes.

Cones

• The volume of a cone can be found by calculating the area of its base (πr^2) and multiplying it by its height (h) divided by 3.
• If a cone has a volume of 240π cubic meters and a height of 5 meters, its radius can be found by rearranging the formula for the volume of a cone.
• If a cone has a volume of 735π cubic millimeters and a height of 5 millimeters, its radius can be found by rearranging the formula for the volume of a cone.

Cylinders

• The radius of a cylinder affects its volume, with a larger radius resulting in a greater volume.
• If a cylinder has a radius of 13 inches and another cylinder has a radius of 10 inches, the taller cylinder will be the one with the larger radius.
• If the diameter of a mug is increased while keeping its height constant, its volume will increase.
• The general relationship between the radius and height in cylinders is that as the radius increases, the volume increases, and as the height increases, the volume also increases.