Volume and Surface Area Concepts

The video tutorial covers the concept of changes in scale, focusing on the surface area and volume of similar solids. It uses real-world examples, such as monuments and a hockey puck, to illustrate how scale factors affect these measurements. Key concepts include the mathematical relationships between scale factors and the surface area and volume of similar figures.

What is the scale factor used to compare the miniature Washington Monument to the real one?

• 1/100

• 1/1,000

• 1/100,000

• 1/10,000

If a similar solid is twice as large as another, how do you calculate its surface area?

• Multiply the original surface area by 2

• Multiply the original surface area by 16

• Multiply the original surface area by 4

• Multiply the original surface area by 8

A rectangular prism has a surface area of 78 square cm. What is the surface area of a similar prism that is three times as large?

• 312 square cm

• 156 square cm

• 702 square cm

• 234 square cm

How is the volume of a similar solid calculated when the scale factor is 1/3?

• Multiply the original volume by 1/9

• Multiply the original volume by 1/27

• Multiply the original volume by 1/3

• Multiply the original volume by 1/81

A triangular prism has a volume of 432 cubic yards. What is the volume of a similar prism reduced to 1/3 of its original size?

• 48 cubic yards

• 16 cubic yards

• 144 cubic yards

• 64 cubic yards

What is the formula for the volume of a cylinder?

• Pi * radius * height

• 2 * Pi * radius * height

• Pi * radius^2 * height

• 2 * Pi * radius^2

If a giant hockey puck is 40 times the size of a standard puck, how do you calculate its volume?

• Multiply the standard puck's volume by 40

• Multiply the standard puck's volume by 40^2

• Multiply the standard puck's volume by 40^3

• Multiply the standard puck's volume by 40^4

What is the surface area of a standard hockey puck if its radius is 1.5 inches and height is 1 inch?

• 7.65 square inches

• 23.55 square inches

• 14.13 square inches

• 9.42 square inches

How do you calculate the surface area of a giant hockey puck that is 40 times the size of a standard puck?

• Multiply the standard puck's surface area by 40^3

• Multiply the standard puck's surface area by 40^2

• Multiply the standard puck's surface area by 40^4

• Multiply the standard puck's surface area by 40

What is the volume of a giant hockey puck if the standard puck's volume is 7.65 cubic inches?

• 452,160 cubic inches

• 30,600 cubic inches

• 76,800 cubic inches

• 12,240 cubic inches