Similar Solids

Front

What are similar solids?

Back

Similar solids are three-dimensional figures that have the same shape but may differ in size. Their corresponding dimensions are proportional.

Front

What is the similarity ratio?

Back

The similarity ratio is the ratio of the lengths of corresponding sides of two similar figures.

Front

If the height of a triangle is doubled, what happens to its area?

Back

The area is doubled.

Front

What is the relationship between the scale factor and the ratio of volumes of similar solids?

Back

The ratio of the volumes of similar solids is the cube of the scale factor.

Front

If two similar cones have a scale factor of 8/27, what is the ratio of their volumes?

Back

512/19683.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the scale factor of two similar figures is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25.

Front

What happens to the area of a shape if all dimensions are multiplied by a factor of k?

Back

The area is multiplied by k^2.

Front

What is the effect on the volume of a shape if all dimensions are multiplied by a factor of k?

Back

The volume is multiplied by k^3.