Evaluating Algebraic Expressions: Substituting Values

This video tutorial covers the concept of substitution in algebraic expressions, focusing on how to replace variables with constants to evaluate expressions. It provides examples of using substitution to calculate the volume of three-dimensional figures, such as cones and cylinders, and includes a conversion of cubic feet to gallons. The tutorial also demonstrates calculating the volume of a sphere and determining the volume when the sphere is half full.

What is the main focus of Unit 3, Lesson 3?

• Learning about linear equations

• Exploring trigonometric functions

• Practicing substitution to evaluate algebraic expressions

• Understanding geometric shapes

What does substitution mean in mathematics?

• Replacing a variable with another variable

• Replacing a variable with an equivalent value, often a constant

• Exchanging one equation for another

• Simplifying an expression without changing variables

In the example where Cohen is 5 inches shorter than Adalie, if Adalie is 36 inches tall, what is Cohen's height?

• 41 inches

• 36 inches

• 5 inches

• 31 inches

How is substitution used in the Pythagorean theorem?

• By replacing the hypotenuse with a constant

• By substituting the lengths of the sides into the formula a^2 + b^2 = c^2

• By using the formula for the area of a triangle

• By changing the formula to a + b = c

What is the formula for the volume of a cone?

• pi * radius^3 * height

• pi * radius^2 * height

• 1/3 * pi * radius^2 * height

• 2/3 * pi * radius^2 * height

If the diameter of a cone's base is 8 inches and the height is 6 inches, what is the radius?

• 8 inches

• 4 inches

• 6 inches

• 2 inches

What is the volume of a cone with a radius of 4 inches and a height of 6 inches?

• 50.24 cubic inches

• 31.4 cubic inches

• 100.48 cubic inches

• 10.48 cubic inches

What is the formula for the volume of a cylinder?

• 2/3 * pi * radius^2 * height

• 1/3 * pi * radius^2 * height

• pi * radius^3 * height

• pi * radius^2 * height

How many gallons are approximately in one cubic foot?

• 12 gallons

• 5 gallons

• 7.5 gallons

• 10 gallons

If a sphere has a diameter of 20 feet, what is its radius?

• 10 feet

• 5 feet

• 20 feet

• 15 feet