Changing Dimensions--SA, V

Front

What is the formula for the volume of a cone?

Back

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

Front

How does the volume of similar cones relate to their radii?

Back

The volumes of similar cones are proportional to the cubes of their corresponding radii.

Front

If the radius of a cone is doubled, how does that affect its volume?

Back

If the radius is doubled, the volume increases by a factor of 8 (2³).

Front

What happens to the surface area of a shape if all dimensions are multiplied by a factor k?

Back

The surface area is multiplied by k².

Front

If the dimensions of a prism are halved, what happens to its volume?

Back

The volume is reduced to 1/8 of the original volume (1/2)³.

Front

What is the relationship between the surface area and volume of a sphere?

Back

The surface area S of a sphere is given by S = 4πr², and the volume V is given by V = (4/3)πr³.

Front

If the surface area of a sphere is increased by a factor of 9, by what factor is the radius increased?

Back

The radius is increased by a factor of 3.

Front

What is the effect on the volume of a prism if all edges are multiplied by 3?

Back

The volume is multiplied by 27 (3³).

Front

How do you calculate the new volume of a prism if its dimensions are reduced by a factor of 1/3?

Back

The new volume is (1/3)³ = 1/27 of the original volume.

Front

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

Back

The surface area A of a cylinder is given by A = 2πr(h + r), where r is the radius and h is the height.