Similar Solids

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 height of a rectangular prism is tripled, how does that affect its volume?

Back

The volume of the prism will also triple if only the height is changed, resulting in a new volume that is three times the original volume.

Front

What happens to the volume of a sphere if its radius is halved?

Back

The volume of a sphere is proportional to the cube of its radius. If the radius is halved, the new volume is (1/2)³ = 1/8 of the original volume.

Front

What is the ratio of the side lengths of two similar figures if their areas are in the ratio of 9:1?

Back

The ratio of the side lengths is the square root of the area ratio. Therefore, √(9:1) = 3:1.

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 the surface areas is the square of the ratio of their volumes. Therefore, (1000:27)^(2/3) = 100:9.

Front

Define similar solids.

Back

Similar solids are three-dimensional shapes that have the same shape but different sizes, with corresponding dimensions in the same ratio.

Front

What is the relationship between the ratios of corresponding sides and the ratios of their volumes in similar solids?

Back

The ratio of the volumes of similar solids is the cube of the ratio of their corresponding sides.

Front

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

Back

The ratio of their volumes will be (1:3)³ = 1:27.

Front

How do you find the volume of a rectangular prism?

Back

The volume of a rectangular prism is found by multiplying its length, width, and height: V = l × w × h.

Front

What is the formula for the volume of a sphere?

Back

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.