Understanding Scale Factors in Geometry

The video tutorial explains the concept of scale factors and their application in geometry. It covers how scale factors affect the dimensions of shapes, specifically focusing on area and volume. The tutorial provides examples of enlarging shapes like rectangles and triangles, demonstrating how to calculate new dimensions and areas using scale factors. It also explains how volume changes with scale factors, using cuboids as examples. The key takeaway is understanding how to apply scale factors to find new lengths, areas, and volumes.

What happens to the side lengths of a rectangle when it is enlarged by a scale factor of 2?

• They are halved.

• They are doubled.

• They are tripled.

• They remain the same.

If a triangle with sides 3, 4, and 5 is enlarged by a scale factor of 5, what will be the length of the longest side?

• 15

• 30

• 20

• 25

How does the area of a shape change when it is enlarged by a scale factor of 3?

• It doubles.

• It remains the same.

• It becomes nine times larger.

• It triples.

A hexagon with an area of 8 square centimeters is enlarged by a scale factor of 3. What is the new area?

• 24 square centimeters

• 72 square centimeters

• 48 square centimeters

• 36 square centimeters

What is the relationship between the scale factor and the new area of a shape?

• The new area is the scale factor times the original area.

• The new area is the scale factor squared times the original area.

• The new area is half the scale factor times the original area.

• The new area is the scale factor cubed times the original area.

When a cuboid is enlarged by a scale factor of 3, how does its volume change?

• It becomes 27 times larger.

• It remains the same.

• It becomes nine times larger.

• It triples.

A cuboid with dimensions 3 cm by 6 cm by 2 cm is enlarged by a scale factor of 3. What is the new volume?

• 108 cubic centimeters

• 972 cubic centimeters

• 324 cubic centimeters

• 648 cubic centimeters

What is the formula for calculating the new volume of a shape when enlarged by a scale factor?

• The new volume is the scale factor times the original volume.

• The new volume is the scale factor squared times the original volume.

• The new volume is the scale factor cubed times the original volume.

• The new volume is half the scale factor times the original volume.

If a box with a volume of 1.5 cubic meters is enlarged by a scale factor of 4, what is the new volume?

• 24 cubic meters

• 96 cubic meters

• 48 cubic meters

• 12 cubic meters

What is the effect of a scale factor of n on the dimensions of a shape?

• The dimensions are multiplied by n.

• The dimensions are multiplied by n squared.

• The dimensions remain unchanged.

• The dimensions are multiplied by n cubed.