Surface Area, Volume and Ratios of Similarity

Front

What is the formula for the volume of a hemisphere?

Back

Volume = (2/3)πr³, where r is the radius.

Front

How do you calculate the surface area of a sphere?

Back

Surface Area = 4πr², where r is the radius.

Front

What is the formula for the volume of a rectangular prism?

Back

Volume = length × width × height.

Front

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

Back

The ratio of surface areas is the square of the ratio of corresponding lengths, and the ratio of volumes is the cube of the ratio of corresponding lengths.

Front

If the volume of a solid is doubled, what happens to its dimensions?

Back

Each dimension is multiplied by the cube root of 2.

Front

What is the formula for the volume of a cylinder?

Back

Volume = πr²h, where r is the radius and h is the height.

Front

How do you find the surface area of a cylinder?

Back

Surface Area = 2πr(h + r), where r is the radius and h is the height.

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3)πr²h, where r is the radius and h is the height.

Front

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

Back

Surface Area = πr(r + l), where r is the radius and l is the slant height.

Front

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

Back

Find the ratio of their corresponding side lengths and square it.