How to solve a word problem involving the cube root

The video tutorial covers solving a geometry problem involving the volume of a sphere. It begins by introducing the formula for volume and emphasizes the importance of identifying and defining variables. The tutorial then demonstrates solving for the radius when given a specific volume and addresses a scenario where the volume is increased by a factor of eight, requiring recalculation of the radius.

What is the first step you should take when approaching a word problem involving equations?

• Solve the equation immediately.

• Ignore the given equation.

• Identify and define the variables.

• Guess the answer.

What does the variable 'v' represent in the formula for the volume of a sphere?

• Diameter

• Circumference

• Radius

• Volume

When given the volume of a sphere as 36π, what is the first step to find the radius?

• Subtract 36

• Divide by 4/3

• Add 4/3

• Multiply by π

How do you solve for the radius when the equation is 36 = 4/3 r³?

• Subtract 4/3

• Divide by 4/3

• Multiply by 4/3

• Multiply by 3/4

If the volume of a sphere is increased by a factor of 8, what happens to the radius?

• It remains the same.

• It doubles.

• It triples.

• It halves.

What is the new volume if the original volume of 36π is increased by a factor of 8?

• 324π

• 288π

• 144π

• 72π

What is the new radius when the volume is increased to 288π?

• 3

• 6

• 9

• 12