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 ratio of the areas of two similar rectangles if the ratio of their corresponding sides is 1:2?

Back

The ratio of the areas is the square of the ratio of the sides. Therefore, (1:2)² = 1:4.

Front

If the volume ratio of two similar solids is 125:64, what is the ratio of their corresponding side lengths?

Back

The ratio of the side lengths is the cube root of the volume ratio. Therefore, the ratio of the side lengths is (125:64)^(1/3) = 5:4.

Front

How do you find the surface area of a larger solid if you know the surface area of a smaller solid and their volume ratio?

Back

Use the formula: Surface Area Ratio = (Volume Ratio)^(2/3). If the volume ratio is 8:27, then the surface area ratio is (8:27)^(2/3) = 4:9.

Front

What is the scale factor of two similar solids if the ratio of their volumes is 27:8?

Back

The scale factor is the cube root of the volume ratio. Therefore, the scale factor is (27:8)^(1/3) = 3:2.

Front

If the surface area of a smaller solid is 36 m² and the volume ratio to a larger solid is 1:8, what is the surface area of the larger solid?

Back

Using the surface area ratio formula: Surface Area Ratio = (Volume Ratio)^(2/3). The surface area of the larger solid is 36 m² * (8)^(2/3) = 36 m² * 4 = 144 m².

Front

What is the relationship between the ratios of corresponding sides, areas, and volumes of similar solids?

Back

The ratio of corresponding sides is 'k', the ratio of areas is 'k²', and the ratio of volumes is 'k³', where 'k' is the scale factor.

Front

If two similar solids have a side length ratio of 1:3, what is the ratio of their volumes?

Back

The volume ratio is (1:3)³ = 1:27.

Front

What is the formula to calculate the surface area of a solid?

Back

The surface area of a solid can vary by shape, but for a rectangular prism, it is SA = 2(lw + lh + wh), where l = length, w = width, h = height.

Front

How do you determine the ratio of the surface areas of two similar solids?

Back

The ratio of the surface areas is the square of the ratio of their corresponding side lengths.