Composite Solids & Changing Dimensions

Front

What is a composite solid?

Back

A composite solid is a three-dimensional shape that is made up of two or more simple geometric shapes, such as cylinders, cones, and prisms.

Front

How do you calculate the volume of a prism?

Back

Volume = Base Area × Height.

Front

What happens to the volume of a prism when each edge is halved?

Back

The new volume is reduced to one-eighth of the original volume.

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) × π × r² × h, where r is the radius and h is the height.

Front

If two shapes are similar, how do their volumes compare?

Back

The ratio of their volumes is the cube of the ratio of their corresponding linear dimensions.

Front

What is the effect on the volume of a cylinder when the radius is doubled?

Back

The volume quadruples.

Front

How do you find the surface area of a composite solid?

Back

Add the surface areas of all the individual shapes that make up the composite solid.

Front

What is the surface area of a cylinder?

Back

Surface Area = 2πr(h + r), where r is the radius and h is the height.

Front

What is the relationship between the dimensions of similar cones?

Back

The ratio of their volumes is equal to the cube of the ratio of their radii.

Front

How do you calculate the volume of a cylinder?

Back

Volume = π × r² × h, where r is the radius and h is the height.