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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

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

Back

It means that for every 3 units of length in one figure, there are 10 units of length in the other figure.

Tags

CCSS.7.G.A.1

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 similar solids?

Back

The ratio of the surface areas of two similar solids is the square of the ratio of their corresponding linear dimensions.

Tags

CCSS.7.G.B.6

Front

If the surface area of a smaller sphere is 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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

How do you calculate the surface area of a larger solid given the surface area of a smaller solid?

Back

Use the ratio of their sides to find the ratio of their surface areas.

Tags

CCSS.7.G.B.6

Front

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

Back

The volume ratio is the cube of the similarity ratio, while the surface area ratio is the square of the similarity 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.