Similar Solids

Front

What are similar solids?

Back

Similar solids are three-dimensional shapes that have the same shape but different sizes. Their corresponding dimensions are proportional.

Front

What is the scale factor in similar solids?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar solids.

Front

How do you find the ratio of volumes of similar solids?

Back

To find the ratio of volumes, cube the ratio of their corresponding side lengths.

Front

If the ratio of side lengths is 2:3, what is the ratio of their volumes?

Back

The ratio of their volumes is 2^3:3^3, which simplifies to 8:27.

Front

What is the relationship between the ratio of areas and the ratio of side lengths?

Back

The ratio of areas of similar figures is the square of the ratio of their corresponding side lengths.

Front

If the ratio of areas of two similar rectangles is 1:4, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

What is the formula for the volume of a sphere?

Back

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Front

If the ratio of the volumes of two spheres is 8:27, what is the ratio of their radii?

Back

The ratio of their radii is 2:3.

Front

How do you calculate the surface area of similar solids?

Back

The ratio of the surface areas of similar solids is the square of the ratio of their corresponding side lengths.

Front

If the ratio of side lengths is 3:1, what is the ratio of their surface areas?

Back

The ratio of their surface areas is 3^2:1^2, which simplifies to 9:1.