Volume Calculations of Cubic Boxes

The video tutorial explains how to calculate the empty space in a cubic box that perfectly fits a ball. It breaks down the problem into three parts: finding the volume of the box, the volume of the ball, and the volume of the empty space. The cubic box has dimensions of 11 inches, and the ball's diameter is also 11 inches. The tutorial demonstrates the calculations for the volumes using formulas for a rectangular prism and a sphere, providing both exact and approximate values. Finally, it calculates the empty space by subtracting the ball's volume from the box's volume.

What is the main problem discussed in the video?

• Determining the weight of a cubic box

• Calculating the empty space in a cubic box with a ball

• Finding the surface area of a sphere

• Measuring the diameter of a ball

What is the formula used to calculate the volume of a cubic box?

• Length x Width

• 2 x (Length + Width + Height)

• Length + Width + Height

• Length x Width x Height

What is the length of each side of the cubic box?

• 10 inches

• 11 inches

• 12 inches

• 13 inches

How is the radius of the ball determined?

• By using the volume formula

• By measuring the circumference

• By halving the diameter

• By doubling the diameter

What is the formula for the volume of a sphere?

• 4/3 πr²

• 4/3 πr³

• 2/3 πr³

• πr³

What is the approximate volume of the ball to the nearest hundredth?

• 697.91 cubic inches

• 696.91 cubic inches

• 698.91 cubic inches

• 695.91 cubic inches

What is the exact volume of the ball in terms of π?

• 1331/5 π cubic inches

• 1331/6 π cubic inches

• 1331/8 π cubic inches

• 1331/7 π cubic inches

How do you calculate the volume of the empty space in the box?

• Multiply the volume of the box by the ball

• Subtract the volume of the ball from the box

• Add the volume of the box and the ball

• Divide the volume of the box by the ball

What is the approximate volume of the empty space in the box?

• 636.09 cubic inches

• 637.09 cubic inches

• 635.09 cubic inches

• 634.09 cubic inches

Why is the equal sign changed to an approximate symbol when calculating the empty space?

• Because the box's volume is an approximation

• Because the ball's volume is an approximation

• Because the box is not a perfect cube

• Because the calculation is incorrect