I am having trouble with this story problem.
Lucy is making a model of a building by using mold, which is in a shape of rectangular prism and open on one side. It has a length of 18 centimeters, a height of 42 centimeters, and a constant thickness on all sides. The model she constructed has a volume of 6160 cubic centimeters. What is the thickness of the mold?
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To find the thickness of the mold, we need to use the formula for the volume of a rectangular prism:
Volume = length x width x height
Given:
- Length = 18 centimeters
- Height = 42 centimeters
- Volume = 6160 cubic centimeters
Let's substitute these values into the formula and solve for the width (thickness):
6160 cubic centimeters = 18 centimeters x width x 42 centimeters
To isolate the width, divide both sides of the equation by (18 centimeters x 42 centimeters):
width = (6160 cubic centimeters) / (18 centimeters x 42 centimeters)
Now, let's calculate the width:
width = 6160 cubic centimeters / (18 centimeters x 42 centimeters)
width ≈ 20 centimeters
Therefore, the thickness of the mold is approximately 20 centimeters.
To find the thickness of the mold, we need to know the formula for the volume of a rectangular prism. The formula is volume = length × width × height. In this case, the length is given as 18 centimeters and the height is given as 42 centimeters. The thickness, however, is unknown, so let's call it "t" centimeters.
The formula for the volume can be rewritten as: 6160 = 18 × width × 42.
To find the width, we divide both sides of the equation by (18 × 42):
6160 ÷ (18 × 42) = width.
So, the width is (6160 ÷ (18 × 42)) centimeters.
Now we can calculate the width.