Geometry SOL Review G.14 Similar Solids

Front

What is the definition of similar solids?

Back

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

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 ratio of their corresponding linear dimensions.

Front

If two similar pyramids have heights of 4 inches and 7 inches, what is the ratio of their volumes?

Back

64:343

Front

What happens to the volume of a rectangular prism if one dimension is doubled while others remain the same?

Back

The volume of the prism becomes twice as large.

Front

What is the formula for the volume of a pyramid?

Back

Volume = (1/3) × Base Area × Height.

Front

How do you calculate the surface area of a rectangular prism?

Back

Surface Area = 2(lw + lh + wh), where l = length, w = width, h = height.

Front

If a pyramid has a surface area of 54 square meters and a volume of 648 cubic meters, what is the surface area of a similar pyramid with a volume of 8232 cubic meters?

Back

294 m²

Front

What is the relationship between the surface areas of similar solids?

Back

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

Front

If two spheres have a scale factor ratio of 1:3, what is the ratio of their surface areas?

Back

The ratio of their surface areas is 1:9.

Front

What is the surface area of a larger sphere if the smaller sphere has a surface area of 16 ft² and the scale factor is 1:3?

Back

144 ft²