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

If the scale factor of two similar solids is 3:1, what does this mean?

Back

It means that for every 3 units of length in the first solid, there is 1 unit of length in the second solid.

Front

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

Back

The ratio of the volumes of similar solids is the cube of the scale factor of their corresponding side lengths.

Front

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

Back

The ratio of their volumes is (8/27)³ = 512/19683.

Front

What is the relationship between the ratio of the volumes and the ratio of the radii of spheres?

Back

The ratio of the volumes of two spheres is the cube of the ratio of their radii.

Front

If the volume ratio 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 volume of a pyramid?

Back

The volume of a pyramid is calculated using the formula V = (1/3) * base area * height.

Front

What is the ratio of the volumes of two similar pyramids with heights of 4 inches and 7 inches?

Back

The ratio of their volumes is (4/7)³ = 64:343.

Front

What is the significance of the ratio of diameters in similar solids?

Back

The ratio of diameters in similar solids is the same as the ratio of their corresponding side lengths.