Volume and Surface Area of Prisms

This video tutorial teaches how to use polynomial long division to find one dimension of a rectangular prism when given the other two dimensions and either the volume or surface area. It explains the formulas for volume and surface area, and provides step-by-step examples of finding the height and length of a prism using polynomial long division.

What is the formula for the volume of a rectangular prism?

• V = l × w × h

• V = l × w

• V = 2(lw + lh + wh)

• V = l + w + h

How is the surface area of a rectangular prism calculated?

• SA = l × w × h

• SA = 2(lw + lh + wh)

• SA = l + w + h

• SA = 2(l + w + h)

Given the volume of a prism as 36x³ + 60x² + x - 20, its length as 3x + 4, and width as 6x + 5, what is the first step to find the height?

• Multiply the length and width

• Subtract the width from the length

• Add the length and width

• Divide the volume by the product of length and width

What is the result of dividing 36x³ by 18x² in the polynomial long division process?

• 18x

• 36x

• 3x

• 2x

What is the height of the rectangular prism when the polynomial division is complete?

• 3x + 1

• 2x - 1

• x + 2

• x - 2

What is the first step in finding the length of a prism using its surface area?

• Divide the surface area by the height

• Multiply the surface area by the width

• Subtract the width from the surface area

• Set up the equation using the surface area formula

In the polynomial long division for length, what is the result of dividing 168x³ by 24x²?

• 6x

• 7x

• 9x

• 8x

What is the length of the rectangular prism after completing the polynomial long division?

• 9x + 2

• 6x - 1

• 7x - 2

• 8x + 1

What is the purpose of using polynomial long division in the context of this lesson?

• To calculate the perimeter of a rectangle

• To solve quadratic equations

• To determine one dimension of a rectangular prism

• To find the area of a circle

Which of the following is NOT a step in polynomial long division?

• Add the divisor to the dividend

• Multiply the divisor by the quotient

• Subtract the result from the dividend

• Divide the leading terms