Volume and Dimensions of Prisms

This video tutorial covers the calculation of volume for rectangular prisms and cubes. It explores the effects of changing dimensions, such as quadrupling the height or halving the side lengths, on the volume. The tutorial also includes writing equations for volume when dimensions are doubled and solving for unknowns in volume equations. A table is used to illustrate how volume changes with different lengths, and the video concludes with determining the volume and height of a box using given data.

What is the volume of a rectangular prism if its base area is 37 cm² and its height is 1/3 cm?

• 12 cm³

• 37 cm³

• 1 3/7 cm³

• 1 9/21 cm³

If the height of a rectangular prism is quadrupled, how does the volume change?

• It doubles

• It quadruples

• It remains the same

• It triples

What equation represents the volume of a prism if the base area is doubled?

• V = 2B + H

• V = B * H

• V = B + 2H

• V = 2B * H

How does the volume of a cube change if all side lengths are halved?

• It becomes one-fourth

• It becomes one-eighth

• It remains the same

• It doubles

What is the volume of a cube with side length 5 1/3 inches?

• 512/27 inches³

• 4096/27 inches³

• 151 19/27 inches³

• 18 26/27 inches³

If the length of a rectangular prism is tripled, what happens to the volume?

• It remains the same

• It quadruples

• It triples

• It doubles

What conclusion can be made about the relationship between the volume and length of a prism?

• Volume is inversely proportional to length

• Volume is directly proportional to length

• Volume is independent of length

• Volume is proportional to the square of the length

What is the volume of box B if the total volume of two boxes is 14.325 cm³ and box A is 5.061 cm³?

• 8.715 cm³

• 9.264 cm³

• 7.215 cm³

• 5.061 cm³

How do you calculate the height of box B if its volume is 8.715 cm³ and the base area is 1.5 cm²?

• Add the base area to the volume

• Subtract the base area from the volume

• Multiply the volume by the base area

• Divide the volume by the base area

What is the height of box B if its volume is 8.715 cm³ and the base area is 1.5 cm²?

• 5.81 cm

• 5.71 cm

• 5.91 cm

• 5.81 cm