Multiplying and dividing monomials 2 | Rational expressions | Algebra II | Khan Academy

TL;DR

To find the height of a cylinder with a volume of 16 pi n to the fifth and a base radius of 2n, divide the volume by the area of the base to get the height.

Transcript

We're asked to find the height of a cylinder with a volume of 16 pi n to the fifth and a base whose radius is 2n. So just as a little bit of review of how you find the volume of a cylinder, let me draw a cylinder here. So if that is the top of my cylinder and that is the height of-- I'm not drawing it as straight as I could. If that is the height o... Read More

Key Insights

• ⌛ The volume of a cylinder is equal to the height times the area of the base.
• 🤨 The area of the base of a cylinder can be calculated using the formula pi times the radius squared.
• ⚾ To find the height of a cylinder, divide the given volume by the area of the base.

Questions & Answers

Q: How is the volume of a cylinder calculated?

The volume of a cylinder is calculated by multiplying its height with the area of its base (either the top or the bottom).

Q: What are the given values in this problem?

The given values are the volume of the cylinder, which is 16 pi n to the fifth, and the radius of the base, which is 2n.

Q: How can the area of the base be calculated?

The area of the base can be calculated using the formula for the area of a circle, which is pi times the radius squared.

Q: How is the height of the cylinder found?

The height of the cylinder is found by dividing the volume by the area of the base, which gives the equation h = (16 pi n to the fifth) / (4 pi n squared).

Summary & Key Takeaways

• The volume of a cylinder is equal to the product of its height and the area of its base.

• The volume of the given cylinder is 16 pi n to the fifth, and the radius of the base is 2n.

• By dividing the volume by the area of the base (4 pi n squared), the height of the cylinder can be determined as 4n to the third power.