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

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

Front

If two similar solids have a scale factor of 2:3, what is the ratio of their volumes?

Back

The ratio of their volumes is (2^3):(3^3) = 8:27.

Front

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

Back

The ratio of the surface areas of similar solids is equal to the square of the scale factor of their corresponding side lengths.

Front

If the surface area of a solid is 54 m² and its volume is 648 m³, what is the scale factor of a similar solid with a volume of 8232 m³?

Back

The scale factor is the cube root of (8232/648), which is 2.

Front

How do you calculate the volume of a similar solid if you know the surface area and volume of the original solid?

Back

Use the ratio of the surface areas to find the scale factor, then cube that scale factor and multiply it by the original volume.

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.

Front

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

Back

The ratio of their heights is also 8:27.

Front

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

Back

The surface area A of a pyramid is given by A = base area + (1/2) * perimeter * slant height.