A rectangular prism has a base that is 4 m by 6 m and a height of 10 m. If all dimensions are doubled, what happens to the volume? Explain the steps that you take to arrive at your answer.
To find the volume of the original rectangular prism, we can use the formula V = lwh, where l is the length, w is the width, and h is the height.
Substituting the given values, we have:
V = (4 m)(6 m)(10 m) = 240 cubic meters
To find the new volume when all dimensions are doubled, we can take each dimension and multiply it by 2. This will give us a new length of 8 m (4 m x 2), a new width of 12 m (6 m x 2), and a new height of 20 m (10 m x 2). Then, we can use the same formula to calculate the new volume:
V = (8 m)(12 m)(20 m) = 1920 cubic meters
Therefore, when all dimensions are doubled, the volume of the rectangular prism increases by a factor of 8 (1920 ÷ 240).
We can see this by looking at the formula for the volume of a rectangular prism. Since volume is calculated by multiplying all three dimensions together, doubling all dimensions results in each dimension getting multiplied by 2. This means that the new volume will be the original volume multiplied by 2 x 2 x 2, or 8.