Basic Geometry and Algebra Concepts

This video tutorial covers Math 8 Unit 5 Lesson 14, focusing on finding cylinder dimensions and calculating volume. It begins with an introduction to the formula for cylinder volume, followed by examples involving different scenarios, such as determining the radius and height of a cylinder given its volume and diameter. The lesson also includes a practical problem involving a cylindrical drink coaster, where students calculate how many coasters are needed to reach a certain height. The tutorial concludes with a review of simplification techniques and solving systems of equations.

What is the formula for the volume of a cylinder?

• Pi * radius^2 * height

• Pi * diameter^2 * height

• Pi * radius * height

• 2 * Pi * radius * height

If a cylinder has a diameter of 4 inches, what is its radius?

• 8 inches

• 2 inches

• 1 inch

• 4 inches

Given a cylinder with a volume of 1632 cubic inches and a height of 24 inches, what is the area of its base?

• 68 square inches

• 1632 square inches

• 102 square inches

• 24 square inches

How do you isolate the term Pi * radius^2 in the equation for the volume of a cylinder?

• Multiply both sides by the height

• Divide both sides by the height

• Add the height to both sides

• Subtract the height from both sides

What is the approximate height of one coaster if its volume is 95.43 cm^3 and radius is 4.5 cm?

• 1.5 cm

• 3.5 cm

• 4.5 cm

• 2.5 cm

How many coasters are needed to reach a height of 7.5 cm?

• 4

• 3

• 5

• 6

What is the result of simplifying the expression 18 / 2?

• 9

• 10

• 11

• 8

What is the simplified result of -25 + 17?

• -8

• 8

• 42

• -42

In solving the system of equations, what is the value of x if -3x = -26?

• 3

• 4

• 1

• 2

What is the y-coordinate if x = 2 in the equation y = 5x - 7?

• 2

• 1

• 3

• 4