Cube Volume and Area Problems

This video tutorial covers Unit 6, Lesson 13 on expressions with exponents. It includes exercises on identifying expressions equal to 3^5, comparing results of different operations by Noah and Diego, determining the truth of various equations, calculating the area and volume of shapes, finding the area of a shaded rectangle, estimating and calculating movie theater ticket sales, and determining the number of panels needed for a garden fence. The lesson emphasizes understanding mathematical operations, expressions, and real-world applications.

Which of the following expressions is equivalent to multiplying three by itself five times?

• 5 times 3

• 5 to the power of 3

• 3 times 5

• 3 to the power of 5

If Noah adds the number 5 four times starting from zero, what is the result?

• 25

• 20

• 15

• 30

Diego starts with 1 and multiplies by 5 four times. What is the final result?

• 125

• 625

• 25

• 100

Is the equation 9 times 9 times 3 equal to 3 to the power of 5 true or false?

• Depends on the context

• Cannot be determined

• False

• True

What is the area of a square with side lengths of three-fifths units?

• 9/25 units squared

• 3/5 units squared

• 15 units squared

• 25 units squared

What is the volume of a cube with edge lengths of two-thirds units?

• 27/8 units cubed

• 2/3 units cubed

• 8/27 units cubed

• 16/27 units cubed

What is the side length of a square with an area of 1/16 square units?

• 1/8 unit

• 1/2 unit

• 1/16 unit

• 1/4 unit

What is the edge length of a cube with a volume of 27/64 cubic units?

• 1/2 unit

• 4/3 unit

• 2/3 unit

• 3/4 unit

If a movie ticket costs $8.50 and the total sales were $29,886, how many tickets were sold?

• 3,000

• 3,516

• 2,986

• 3,200

How many panels are needed to fence a garden that is 8.5 feet by 6.33 feet if each panel is 2/3 of a foot wide?

• 43

• 46

• 45

• 44