Volume and Scale Factor Problems

The video tutorial covers the concepts of scaling and dilation in geometry, focusing on how these transformations affect area and volume. It explains the mathematical relationships between original and new dimensions when a shape is scaled, using examples like a rectangular prism box and a banner design. The tutorial also addresses common errors in volume calculations and demonstrates how to graph the effects of scale factors. Additionally, it explores the geometry of hexagons and circles, and explains why lines perpendicular to the same line are parallel.

If a rectangular prism box originally requires 2 oz of paint, how much paint is needed when its dimensions are doubled?

• 4 oz

• 6 oz

• 8 oz

• 10 oz

When the dimensions of a box are doubled, how many cups of sugar can it hold if it originally held 15 cups?

• 120 cups

• 90 cups

• 60 cups

• 30 cups

What is the new volume of a solid with an original volume of 12 units when dilated by a scale factor of 1/4?

• 0.75 units

• 1.5 units

• 3 units

• 18 units

If a solid with a volume of 12 units is dilated by a scale factor of 4, what is the new volume?

• 192 units

• 1024 units

• 768 units

• 48 units

Kieran calculated the volume of a dilated solid incorrectly. What mistake did he make?

• Used K squared instead of K

• Used K instead of K squared

• Used K instead of K cubed

• Used K cubed instead of K squared

What is the correct volume of a solid with an original volume of 10 cubic units when dilated by a scale factor of 3.5?

• 428.75 cubic units

• 35 cubic units

• 500 cubic units

• 85 cubic units

How do you calculate the scale factor needed to achieve a new area for a parallelogram?

• Square of new area divided by original area

• Divide new area by original area

• Square root of new area divided by original area

• Multiply new area by original area

What is the scale factor if the new area of a parallelogram is 160 square ft and the original area is 10 square ft?

• 2

• 4

• 6

• 8

Which of the following points is on the graph if the equation represents the scale factor needed for a figure to achieve a certain area?

• (8, 2)

• (0, 0)

• (1, 1)

• (4, 1)

What is the area of a banner if its design with an area of 1.5 square ft is dilated by a scale factor of 5?

• 25 square ft

• 37.5 square ft

• 7.5 square ft

• 15 square ft