Question
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.
What is the height of the second rectangular prism? Enter the answer in the box.
Answers
GPT 3.5
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}.
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}.