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 similarity ratio?

Back

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

Front

If two solids are similar with a similarity ratio of 3:10, what does this mean?

Back

It means that for every 3 units of length in the first solid, there are 10 units of length in the second solid.

Front

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

Back

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

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

What is the formula for the surface area of a sphere?

Back

The surface area (SA) of a sphere is given by the formula SA = 4πr², where r is the radius.

Front

How do you find the surface area ratio of two similar solids?

Back

The surface area ratio is the square of the similarity ratio of their corresponding linear dimensions.

Front

If a smaller sphere has a surface area of 16 ft² and the scale factor is 1:3, what is the surface area of the larger sphere?

Back

The surface area of the larger sphere is 144 ft².

Front

What is the relationship between the volume and surface area of similar solids?

Back

For similar solids, the ratio of their volumes is the cube of the ratio of their corresponding lengths, while the ratio of their surface areas is the square of that ratio.

Front

If the volume of a prism is 1000 cm³ and a similar prism has a volume of 27 cm³, what is the ratio of their surface areas?

Back

The ratio of their surface areas is 100:9.