Exploring Unit Eleven: Pages 19-20 Concepts

The video tutorial covers the use of proportions and scale factors to solve geometry problems, including calculating surface area and volume. It explains the effects of changing dimensions on these calculations and provides examples using different shapes such as prisms, cones, and spheres. The tutorial emphasizes understanding the relationships between linear dimensions, surface area, and volume, and how these relationships change with scaling.

What is the scale factor if the ratio of the diameters of two similar figures is 3 to 5?

• 1 to 2

• 27 to 125

• 9 to 25

• 3 to 5

If the surface area of the smaller figure is 378, what is the surface area of the larger figure given the scale factor is 3 to 5?

• 945

• 9450

• 1050

• 105

Given the surface areas of two similar figures are 108 and 147, what is the scale factor?

• 4 to 3

• 36 to 49

• 3 to 2

• 6 to 7

If the dimensions of a solid are doubled, by what factor does the surface area change?

• 16

• 8

• 4

• 2

What is the new surface area if the original surface area is 62 and the dimensions are multiplied by 5?

• 310

• 620

• 1550

• 3100

If the volume of a figure is 972 and the dimensions are multiplied by 2/3, what is the new volume?

• 648

• 288

• 216

• 432

How many times larger is the volume of a cylinder if its height is doubled?

• 8 times

• 16 times

• 4 times

• 2 times

How many times larger is the volume of a square pyramid if the base is tripled?

• 12 times

• 9 times

• 3 times

• 6 times

If the radius of a sphere is halved, how many times smaller is the surface area?

• 16 times

• 2 times

• 4 times

• 8 times

How many times larger is the volume of a cone if the radius is multiplied by 6?

• 6 times

• 36 times

• 12 times

• 18 times