Exploring Scale Factors in Ratio and Proportions

The video tutorial explains the concept of scale factors, including linear, area, and volume scale factors. It provides examples of how to calculate these factors and applies them to geometry and unit conversion. The tutorial also highlights the importance of understanding scale factors in various contexts, such as enlarging shapes and converting units in the metric system.

What does a linear scale factor of 2 indicate about the size of a new shape compared to the original?

• The new shape is four times the size of the original.

• The new shape is the same size as the original.

• The new shape is twice the size of the original.

• The new shape is half the size of the original.

If a shape's linear scale factor is 0.5, what is the size of the new shape relative to the original?

• Twice the size

• Four times smaller

• The same size

• Half the size

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

• 6 times the original area

• The same as the original area

• 3 times the original area

• 9 times the original area

What is the area of a rectangle enlarged by a scale factor of 4, if the original dimensions were 2 cm by 5 cm?

• 20 cm squared

• 160 cm squared

• 80 cm squared

• 40 cm squared

If a rectangle's area is originally 50 cm squared and it is enlarged by a scale factor of 2, what is the new area?

• 50 cm squared

• 400 cm squared

• 200 cm squared

• 100 cm squared

If a cube's edge is enlarged by a scale factor of 2, what is the new volume?

• 16 cm cubed

• 8 cm cubed

• 4 cm cubed

• 2 cm cubed

Calculate the volume of a cuboid with original dimensions 2 cm x 3 cm x 4 cm, scaled by a factor of 3.

• 72 cm cubed

• 216 cm cubed

• 54 cm cubed

• 108 cm cubed

What is the volume of a shape if it is enlarged by a scale factor of 5 and the original volume was 100 cm cubed?

• 12500 cm cubed

• 625 cm cubed

• 500 cm cubed

• 2500 cm cubed

How many milliliters are in 3 liters?

• 300 milliliters

• 3000 milliliters

• 30 milliliters

• 0.3 milliliters

Convert 2 kilometers to millimeters.

• 2000000 millimeters

• 20000 millimeters

• 2000 millimeters

• 200 millimeters