Two rectangular prisms have the same volume. The first prism has a length of 10 meters, a width of 6 meters, and a height of 2 meters. The second prism has a length of 6 meters and a width of 4 meters.
What is the height of the second rectangular prism? Enter the answer in the box.
To find the height of the second rectangular prism, we can use the formula for volume of a rectangular prism:
Volume = Length * Width * Height
Since the two prisms have the same volume, we can set up the equation:
10 * 6 * 2 = 6 * 4 * height
Simplifying this equation:
120 = 24 * height
Dividing both sides by 24:
5 = height
Therefore, the height of the second rectangular prism is 5 meters.
The volume of a rectangular prism is given by the formula: length x width x height.
The volume of the first prism is: 10 meters x 6 meters x 2 meters = 120 cubic meters.
Since the two prisms have the same volume, the volume of the second prism is also 120 cubic meters.
Let's denote the height of the second prism as h. Therefore, the volume equation for the second prism is: 6 meters x 4 meters x h = 120 cubic meters.
Simplifying the equation, we have: 24h = 120.
Dividing both sides of the equation by 24, we find: h = 120 / 24 = <<120/24=5>>5.
Therefore, the height of the second rectangular prism is 5 meters. Answer: \boxed{5}.
To find the height of the second rectangular prism, we can use the formula for volume of a rectangular prism: V = lwh, where l is the length, w is the width, and h is the height.
We already know the volume of both prisms is the same, so we can set up an equation with the given values.
For the first prism with a length of 10 meters, a width of 6 meters, and a height of 2 meters:
V1 = 10 * 6 * 2 = 120 cubic meters
For the second prism with a length of 6 meters and a width of 4 meters, we want to find the height (h2):
V2 = 6 * 4 * h2 = 120 cubic meters
Now, we can solve for h2 by rearranging the equation:
24h2 = 120
Dividing both sides by 24, we get:
h2 = 120 / 24 = 5 meters
Therefore, the height of the second rectangular prism is 5 meters.