Isolating Variables and Volume Formulas

The video tutorial explains how to isolate a variable, specifically the radius (R), from the volume formula of a sphere. It covers the multiplication of numbers and variables, converting terms into fractions, and applying multiplication rules. The tutorial guides through rearranging the formula, moving terms across the equation using division, and finally isolating R by taking the cube root.

What is the formula for the volume of a sphere?

• V = 4/3 πr^3

• V = 2πr

• V = 4πr^2

• V = πr^2

What is the first step in isolating a variable in an equation?

• Multiply all terms by zero

• Divide by the variable

• Rearrange the equation

• Add all terms together

How do you multiply fractions?

• Divide the numerators by the denominators

• Subtract the numerators and add the denominators

• Multiply the numerators and denominators separately

• Add the numerators and denominators

What does 4π represent in the context of the sphere's volume formula?

• An unknown value

• A fraction

• A constant number

• A variable

What operation is used to move a term from one side of an equation to the other?

• Addition

• Subtraction

• Exponentiation

• Multiplication or Division

What is the opposite operation of cubing a number?

• Taking the cube root

• Multiplying by three

• Taking the square root

• Squaring

What is the result of dividing 3V by 4π in the context of isolating R?

• R cubed

• R to the power of four

• R squared

• R to the power of five

What is the final step to solve for R in the equation?

• Multiply both sides by 3

• Subtract 3V from both sides

• Add 4π to both sides

• Take the cube root of both sides

Why is it important to keep terms in symbolic form during calculations?

• To make it harder to solve

• To simplify the equation

• To make the equation longer

• To avoid large decimals

What does isolating a variable help you find in an equation?

• The product of all terms

• The difference between terms

• The value of the variable

• The sum of all terms