Understanding the Volume of a Cylinder

The video tutorial explains how to define a polynomial for the volume of a right circular cylinder. It starts by introducing the volume formula, V = πr²h, and applies it to a cylinder with a radius of t + 6 cm and a height of 3 cm. The tutorial then expands the polynomial expression by squaring the binomial and combining like terms. Finally, it presents the simplified volume expression both with and without units, emphasizing the importance of understanding each step in the process.

What is the formula for the volume of a right circular cylinder?

• pi r-squared h

• pi r h

• 2 pi r h

• pi r-squared

In the given figure, what is the expression for the radius?

• t plus six centimeters

• t squared centimeters

• six t centimeters

• t minus six centimeters

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

• t plus six centimeters

• Six centimeters

• Three centimeters

• t centimeters

What property allows us to change the order of multiplication in the expression?

• Distributive property

• Associative property

• Commutative property

• Identity property

When squaring a binomial, what is the first step?

• Square each term separately

• Distribute each term of the first binomial to each term of the second

• Add the terms directly

• Multiply the coefficients only

What is the result of combining the like terms 6t and 6t?

• 36

• t squared

• 6t

• 12t

What is the coefficient of t-squared in the final polynomial expression?

• 12 pi

• 108 pi

• 36 pi

• 3 pi

What is the final term in the polynomial expression for the volume?

• 12 pi

• 3 pi

• 36 pi

• 108 pi

What are the units of the volume in the final expression with units?

• Meters cubed

• Centimeters cubed

• Centimeters squared

• Centimeters

What is the complete polynomial expression for the volume without units?

• 3 pi t-squared plus 36 pi t plus 108 pi

• 108 pi t-squared plus 36 pi t plus 3 pi

• 3 pi t plus 36 pi t-squared plus 108 pi

• 36 pi t-squared plus 3 pi t plus 108 pi