Volume and Polynomial Expressions

The video tutorial explains how to find the volume of a cylindrical tank. It begins by introducing the problem and visualizing the tank. The base area and height are given as algebraic expressions. The volume is calculated by multiplying the base area by the height. The distributive property is applied to simplify the resulting polynomial expression. The final volume is expressed as a polynomial in terms of x.

What is the base area of the tank in terms of x?

• 225x squared

• 24x to the third

• 8x minus 5

• 3x squared plus 30x plus 5

What shape is the tank assumed to be?

• Rectangular prism

• Sphere

• Cylinder

• Cone

How do you calculate the volume of a three-dimensional object like the tank?

• Subtract the height from the base area

• Multiply the base area by the height

• Divide the base area by the height

• Add the base area and height

What mathematical property is used to multiply the base area and height?

• Commutative property

• Distributive property

• Associative property

• Identity property

What is the result of multiplying 8x by 3x squared?

• 15x squared

• 240x squared

• 24x to the third

• 24x squared

What is the simplified form of the x squared terms in the volume expression?

• 240x squared

• 15x squared

• 110x squared

• 225x squared

What is the coefficient of the x term in the final volume expression?

• 40

• -110

• 150

• 25

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

• -5

• 0

• 25

• -25

What is the degree of the polynomial expression for the volume of the tank?

• First degree

• Second degree

• Third degree

• Fourth degree

What is the final expression for the volume of the tank?

• 24x to the third plus 225x squared minus 110x minus 25

• 8x minus 5

• 3x squared plus 30x plus 5

• 240x squared plus 40x minus 25