Exploring Adding and Subtracting Rational Expressions

The video tutorial covers the calculation of the volume of a cylinder using the formula pi times radius squared times height. It explains how to leave the volume in terms of pi for accuracy and demonstrates the effect of doubling the radius or height on the volume. Practical applications include determining if sand can fill a vase and calculating the volume of juice concentrate. The tutorial also shows how to find the radius from a given volume.

What is the formula for the volume of a cylinder?

• pi * radius + height

• pi + radius^2 + height

• 2 * pi * radius * height

• pi * radius^2 * height

If the radius of a cylinder is 5 cm and the height is also 5 cm, what is the volume in terms of pi?

• 125 pi cm^3

• 75 pi cm^3

• 100 pi cm^3

• 25 pi cm^3

When solving for the volume of a cylinder in terms of pi, what do you do with pi in your final answer?

• Ignore it

• Multiply it by 3.14

• Leave it as is

• Divide by pi

What is the volume of a cylinder with a radius of 6 cm and height of 6 cm, in terms of pi?

• 216 pi cm^3

• 36 pi cm^3

• 108 pi cm^3

• 72 pi cm^3

How does the volume change when the radius of a cylinder is doubled?

• Quadruples

• Triples

• Remains the same

• Doubles

For a cylinder with a doubled height, how does the volume change?

• Doubles

• Quadruples

• Remains the same

• Triples

If the diameter of a cylinder is 2.5 inches, what is the radius?

• 5 inches

• 2.5 inches

• 0.625 inches

• 1.25 inches

If you have three cylindrical bottles of sand with a total volume of 55.2 cubic inches, can you fill a vase of 47.5 cubic inches?

• Exactly, no sand left

• No, not enough sand

• Yes, with some sand left

• Yes, perfectly

When preparing juice, if you add three cans of water to one can of concentrate, how many cans of liquid do you have?

• One can

• Two cans

• Four cans

• Three cans

If the volume of a cylinder is given and you need to find the radius, which operation is not required?

• Square root

• Subtraction

• Division

• Multiplication