Volume and Simplification Concepts

The video tutorial explains how to calculate the volume of a sphere using the formula 4/3 πr³. It walks through the process of simplifying the formula by including exponents, cubing the cube root, and simplifying common factors. The tutorial concludes with the final calculation, resulting in a volume of nine cubic units.

What is the formula for the volume of a sphere?

• πr³

• 4/3 πr³

• 4/3 πr²

• 2/3 πr³

In the given problem, what is the expression for the volume of the sphere before simplification?

• 4/3 π x (cube root of 16π²) / 4π³

• 4/3 π x 16π²

• 4/3 π x (cube root of 16π²)

• 4/3 π x 3

What happens when you cube the cube root of a number?

• It returns the original number

• It squares the number

• It doubles the number

• It halves the number

How do you simplify an expression with powers raised to powers?

• Add the exponents

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

What is the result of simplifying 4 divided by 4?

• 4

• 2

• 1

• 0

When simplifying, what happens to a factor that appears in both the numerator and the denominator?

• It cancels out

• It is squared

• It is doubled

• It is added

What is the simplified form of 3 cubed divided by 3?

• 9

• 3

• 27

• 1

What is the final volume of the sphere in cubic units?

• 16

• 4

• 27

• 9

What is the simplified form of pi squared divided by pi squared?

• 0

• π²

• 1

• π

What is the result of dividing nine by one?

• Nine

• Zero

• One

• Three