a rectangular prism has a length of 6 inches and a volume of 120 cubic inches. the length of this prism changed to 3 inches and the other dimensions stayed the same. What is the volume of the prism after the change
L * W = 120
6W = 120
3W = ?
To solve this problem, we can use the formula for the volume of a rectangular prism. The formula is:
Volume = length × width × height
Given that the initial length of the prism is 6 inches and the volume is 120 cubic inches, we can substitute the values into the formula to find the initial width and height.
120 = 6 × width × height
Dividing both sides of the equation by 6, we get:
20 = width × height
Since the length has changed to 3 inches and the other dimensions remain the same, we can substitute the new length value into the equation:
Volume = 3 × width × height
Now, we need to find the new volume. To do this, we can substitute the values into the formula:
New Volume = 3 × width × height
Since we know that the initial volume was 120 cubic inches, we can substitute this into the formula:
120 = 3 × width × height
Dividing both sides of the equation by 3, we get:
40 = width × height
Therefore, the volume of the prism after the change is 40 cubic inches.
To find the volume of the prism after the change, we need to use the formula for the volume of a rectangular prism, which is length × width × height.
Given:
Original length = 6 inches
Original volume = 120 cubic inches
Let's assume the original width and height are w and h, respectively.
Using the formula, we have:
6 inches × w inches × h inches = 120 cubic inches
Now, the length changes to 3 inches, and the other dimensions (width and height) remain the same. Let's call the new volume V.
3 inches × w inches × h inches = V
Since the question states that the width and height stay the same, we know that w and h are the same as before.
So, the new volume, V, is equal to the original volume divided by the original length and multiplied by the new length. Thus, we have:
V = (Original volume / Original length) × New length
V = (120 cubic inches / 6 inches) × 3 inches
Simplifying this calculation, we get:
V = 20 cubic inches × 3 inches
V = 60 cubic inches
Therefore, the volume of the prism after the change is 60 cubic inches.