Understanding Changes in Dimensions and Volume

The video tutorial explains how to describe changes in the radius of a cylindrical can when either its height or volume changes, while maintaining a constant volume. It introduces the concepts of absolute change and scale factor using a tree height example. The problem of redesigning a bubble gum can is presented, where the can's height is increased fourfold, and the new radius is calculated. Additionally, the tutorial explores the scenario where the can's volume is increased fourfold, and the corresponding new radius is determined. The lesson emphasizes careful expression and interpretation of changes.

What remains constant when describing the change in the radius of a can if its height changes?

• Volume

• Height

• Surface Area

• Radius

How is absolute change in height calculated?

• By adding the old and new heights

• By multiplying the old height by the new height

• By subtracting the old height from the new height

• By dividing the new height by the old height

If a tree grows from 4 feet to 8 feet, what is the scale factor of its growth?

• 1 time

• 8 times

• 2 times

• 4 times

What is a common mistake when describing the change in height of a tree?

• Saying the tree is 4 times taller

• Saying the tree is 2 times taller

• Saying the tree is 8 feet tall

• Saying the tree is 4 feet taller

What is the formula used to find the radius of a cylindrical can?

• r = sqrt(v / pi h)

• r = v / pi h

• r = pi h / v

• r = v * pi h

If the height of a cylindrical can is increased four times, what happens to the radius?

• It quadruples

• It halves

• It remains the same

• It doubles

What is the new radius if the original radius of a can is 6 inches and the height is increased four times?

• 12 inches

• 3 inches

• 9 inches

• 6 inches

If the volume of a can is increased four times, what happens to the radius?

• It doubles

• It halves

• It quadruples

• It remains the same

What is the new radius if the original radius is 6 inches and the volume is increased four times?

• 24 inches

• 6 inches

• 18 inches

• 12 inches

What is the key takeaway from the lesson on changing dimensions and volume?

• Understand the effect of changing one part of an expression

• Always increase both height and volume

• Focus only on volume changes

• Keep the radius constant