Understanding Volume and Cubes

This video tutorial covers the seventh-grade concept of volume, focusing on calculating the volume of rectangular prisms and cubes. It begins with a review of the basic volume formula, volume equals base times height, and explains how to solve for missing dimensions, such as height, when given the volume and base area. The tutorial also explores the special case of cubes, where all sides are equal, and introduces the concept of cube roots to find side lengths when given the volume.

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

• Length x Width

• Base x Height

• Length + Width + Height

• Width x Height

How can the base of a rectangular prism be calculated?

• By subtracting height from length

• By multiplying length and width

• By adding length and width

• By dividing width by height

If a rectangular prism has a volume of 900 cubic inches and a base of 75 square inches, what is the height?

• 10 inches

• 18 inches

• 15 inches

• 12 inches

What is a unique characteristic of a cube compared to other rectangular prisms?

• All sides are the same length

• All faces are rectangles

• All sides are different lengths

• It has no volume

What does 's cubed' represent in the context of a cube's volume?

• Side / Side

• Side x Side x Side

• Side x Side

• Side + Side + Side

In the context of volume, what does the term 'cubed' signify?

• Multiplying a number by itself twice

• Dividing a number by itself

• Multiplying a number by itself three times

• Adding a number to itself three times

Which of the following is NOT a property of a cube?

• All faces are squares

• It has different lengths for each side

• It has six faces

• All edges are equal

If a cube has a volume of 125 cubic meters, what is the length of one side?

• 5 meters

• 4 meters

• 6 meters

• 3 meters

What mathematical operation is used to find the side length of a cube from its volume?

• Square root

• Cube root

• Subtraction

• Addition

What is the result of 5 x 5 x 5?

• 100

• 125

• 150

• 175