Cylinder Volume and Height Calculations

The video tutorial explains how to find the height of a cylinder given its volume and the radius of its base. It begins with a review of the formula for the volume of a cylinder, which is the product of the height and the area of the base. The tutorial then guides viewers through the process of solving for the height by substituting the given values into the formula and simplifying the resulting equation. The final solution shows that the height of the cylinder is 4n to the third power.

What is the given volume of the cylinder in the problem?

• 4 pi n to the fifth

• 32 pi n to the fifth

• 16 pi n to the fifth

• 8 pi n to the fifth

What is the radius of the base of the cylinder as given in the problem?

• 3n

• n

• 4n

• 2n

What is the formula for the volume of a cylinder?

• Volume = height - area of base

• Volume = height / area of base

• Volume = height + area of base

• Volume = height * area of base

How do you calculate the area of a circle?

• Area = pi * radius squared

• Area = pi * radius

• Area = pi * radius cubed

• Area = pi * diameter

What is the area of the base of the cylinder in terms of n?

• 2 pi n squared

• 4 pi n squared

• 16 pi n squared

• 8 pi n squared

What is the first step in solving for the height of the cylinder?

• Multiply both sides by 4 pi n squared

• Add 4 pi n squared to both sides

• Divide both sides by 4 pi n squared

• Subtract 4 pi n squared from both sides

What happens to the pi terms when simplifying the equation for height?

• They remain unchanged

• They are multiplied together

• They cancel each other out

• They are added together

What is the simplified expression for the height of the cylinder?

• 8n to the third power

• 4n to the third power

• 16n to the third power

• 2n to the third power

What operation is performed on the exponents of n when simplifying the height equation?

• Multiplication

• Division

• Addition

• Subtraction

What is the final height of the cylinder in terms of n?

• 2n to the third power

• 4n to the third power

• 6n to the third power

• 8n to the third power