Exploring the Impact of Linear Dimension Changes on Volume and Surface Area

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

• The volume remains the same.

• The volume doubles.

• The volume increases by a factor of eight.

• The volume quadruples.

What mathematical operation is used to find the new volume when the radius of a sphere is doubled?

• Multiplication

• Division

• Addition

• Exponentiation

How does quadrupling the side length of a cube affect its surface area?

• Doubles the surface area.

• No change to the surface area.

• Increases by a factor of four.

• Increases by a factor of sixteen.

What constant is used in the formula for calculating the surface area of a cube?

• 8

• 6

• 4

• π (Pi)

If the base of a triangle is tripled and the height remains the same, how does the area change?

• Remains unchanged.

• Increases by a factor of nine.

• Doubles in size.

• Triples in size.

In the formula for the area of a triangle, which component remains constant when the base is tripled?

• The base

• The height

• The area

• 1/2

What is the effect on the volume of a cone if its height is increased eightfold?

• Doubles in volume.

• Increases by a factor of four.

• Increases by a factor of eight.

• No change in volume.

When the height of a cone is increased eightfold, which part of the volume formula is directly affected?

• 1/3

• The radius

• π (Pi)

• The height

By what factor does the volume of a cylinder increase if its radius is multiplied by seven?

• Increases by a factor of seven.

• Increases by a factor of forty-nine.

• Triples in volume.

• Doubles in volume.

What mathematical operation is applied to the radius in the formula for the volume of a cylinder when it is multiplied by seven?

• Multiplication

• Addition

• Exponentiation

• Subtraction