Volume and Scale Factor Problems

The video tutorial covers the concept of dilation in geometry, focusing on calculating scale factors for volume and surface area changes. It explains how to determine the scale factor K by comparing new and original volumes or areas, using cube and square roots. The tutorial also includes graphing exercises to identify points on scale factor equations and practical applications like calculating wrapping paper needed for a box and resizing a flyer. Additionally, it covers calculating side lengths in a 45-45-90 triangle.

What is the scale factor K if a solid with an original volume of 8 cubic units is dilated to a new volume of 216 cubic units?

• 2

• 3

• 5

• 4

If a solid's volume changes from 8 cubic units to 1 cubic unit, what is the value of K?

• 1/5

• 1/4

• 1/3

• 1/2

A solid's volume increases from 8 cubic units to 1000 cubic units. What is the scale factor K?

• 5

• 6

• 7

• 8

Which point is on the graph if the volume of a solid is 7 cubic units and the scale factor is determined by the cube root of V/7?

• (14,2)

• (7,1)

• (1,1)

• (0,0)

What is the scale factor K if a solid's surface area changes from 8 square units to 512 square units?

• 6

• 8

• 7

• 9

If a solid's surface area remains the same after dilation, what is the scale factor K?

• 3

• 1

• 0

• 2

How many rolls of wrapping paper are needed if a box's dimensions are tripled and originally required 1/8 of a roll?

• 1 and 1/8

• 1

• 1 and 1/2

• 1 and 1/4

What is the new volume of a box if its original volume is 10 cubic inches and its dimensions are tripled?

• 300

• 270

• 200

• 100

What is the new volume of a solid with an original volume of 8 cubic units and a scale factor of 1.5?

• 18

• 27

• 12

• 36

If a solid's volume is 8 cubic units and the scale factor is 0.6, what is the new volume?

• 2.5

• 3.6

• 4.8

• 1.728