Scale Factors and Volume Calculations

The video tutorial covers various mathematical problems involving dilation and scale factors. It includes examples such as calculating the scale factor for a muffin to serve more people, determining the scale factor for a travel version of a board game box, and finding the new volume of a dilated cone. Additionally, it explores the scale factor for a model oil truck to a full-size truck, graphing scale factors, and calculating the surface area and volume of a cube and its dilation. The tutorial concludes with determining the scale factor for a dilated circle's area.

If a muffin is dilated to serve 100 people instead of 1, what is the scale factor for the volume?

• 3.2

• 100

• 4.6

• 10

How much more decorative paper is needed for the larger muffin?

• 10 times

• 21.5 times

• 15 times

• 5 times

What is the scale factor for the travel version of the board game box?

• 0.14

• 0.5

• 0.375

• 0.25

How tall will the travel version of the board game box be?

• 5 cm

• 3 cm

• 8 cm

• 2 cm

What is the new volume of the dilated cone?

• 2250 Pi in³

• 9112.5 Pi in³

• 1125 Pi in³

• 800 Pi in³

What is the scale factor for the full-size oil truck model?

• 10

• 15

• 20

• 25

What is the scale factor for a solid with a volume of 4 cubic units to obtain a volume of V cubic units?

• 4/V

• V/4

• Square root of V/4

• Cube root of V/4

What is the surface area of a cube with an edge length of 3 inches?

• 36 in²

• 27 in²

• 54 in²

• 45 in²

What is the volume of a cube with an edge length of 3 inches?

• 54 in³

• 18 in³

• 36 in³

• 27 in³

What is the new surface area of the cube after dilation by a scale factor of 0.5?

• 9 in²

• 27 in²

• 13.5 in²

• 54 in²