Scaling Factors in Geometry

The video tutorial covers the concept of scale factor and its application in geometry problems. It explains how to calculate changes in dimensions, area, and volume when objects are scaled. Three problems are solved: determining the volume change of a cube with doubled edges, calculating the perimeter of an enlarged starfish image, and finding the diameter of an ice cream scoop for half the volume. The tutorial emphasizes the importance of understanding scale factor formulas for quick problem-solving.

What happens to the volume of a cube if each edge is doubled in length?

• It doubles.

• It remains the same.

• It quadruples.

• It increases eightfold.

Which formula is used to calculate the new volume when scaling an object?

• Multiply by the scale factor to the fourth power.

• Multiply by the scale factor cubed.

• Multiply by the scale factor squared.

• Multiply by the scale factor.

If the scale factor for length is 2, what is the scale factor for volume?

• 6

• 4

• 8

• 2

What is the perimeter of a starfish if its original perimeter is 30 cm and the area is scaled by a factor of 9?

• 30 cm

• 60 cm

• 270 cm

• 90 cm

How do you calculate the new perimeter when scaling an image?

• Multiply by the scale factor cubed.

• Multiply by the scale factor squared.

• Divide by the scale factor.

• Multiply by the scale factor.

If Tim's ice cream scoop has a diameter of 2 inches, what should be the diameter of Paul's scoop if he wants half the volume?

• 1.26 inches

• 1 inch

• 2 inches

• 1.59 inches

What is the relationship between the scale factor for volume and the scale factor for length?

• Volume scale factor is the square of length scale factor.

• Volume scale factor is the cube of length scale factor.

• Volume scale factor is the fourth power of length scale factor.

• Volume scale factor is the same as length scale factor.