3. The architect determines that the volume of Building A and Building B will be different if the measurements are the same, like in the image.
The architect considers changing the height of Building B. What would the height of Building B have to become so that Building B has the same volume as Building A? Show how to use the formula for the volume of Building B to determine the answer.
(4 points)
Let's first determine the volume of Building A using the formula for the volume of a rectangular prism, which is V = l * w * h:
Building A:
Volume = 10 * 5 * 6
Volume = 300 cubic units
Now, let's use the same formula to find the volume of Building B with the changed height (let's call it h'):
Building B:
Volume = 5 * 6 * h'
Volume = 30h' cubic units
Since we want Building B to have the same volume as Building A, we can set the two volume equations equal to each other:
30h' = 300
Now, solve for h':
h' = 300 / 30
h' = 10
Therefore, the height of Building B would have to become 10 units in order for Building B to have the same volume as Building A.