Each of two trapezoidal prisms has a volume of 120 cubic centimeters. The prisms have no dimensions in common. Give possible dimensions for each prism.
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http://hubpages.com/education/Volume-of-a-Trapezoidal-Prism-Formula-and-Examples
so you have a number of choices for dimensions.
To find the possible dimensions for each trapezoidal prism, we need to consider the formula for calculating the volume of a trapezoidal prism.
The formula for the volume of a trapezoidal prism is:
Volume = ((a + b) / 2) * h * l,
where:
- 'a' and 'b' are the lengths of the bases of the trapezoid,
- 'h' is the height of the trapezoid,
- 'l' is the length of the prism.
Since we are given that the volume of each prism is 120 cubic centimeters, we can set up the following equation for each prism:
120 = ((a + b) / 2) * h * l.
Now, let's consider some possibilities for the dimensions of each prism.
Prism 1:
We can start with arbitrary values to find one set of possible dimensions for the first prism. For example, let's assume the first prism has:
- Base lengths of a = 5 cm and b = 8 cm,
- A height of h = 6 cm.
Now we can find the length l that satisfies the equation:
120 = ((5 + 8) / 2) * 6 * l,
120 = (13 / 2) * 6 * l,
120 = 39 * l,
l = 120 / 39,
l ≈ 3.08 cm.
So, one possible set of dimensions for prism 1 is a = 5 cm, b = 8 cm, h = 6 cm, and l ≈ 3.08 cm.
Prism 2:
Since the prisms have "no dimensions in common," we need to choose different dimensions for the second prism. Let's assume the second prism has:
- Base lengths of a = 3 cm and b = 10 cm,
- A height of h = 8 cm.
Now we can find the length l that satisfies the equation:
120 = ((3 + 10) / 2) * 8 * l,
120 = (13 / 2) * 8 * l,
120 = 52 * l,
l = 120 / 52,
l ≈ 2.31 cm.
So, one possible set of dimensions for prism 2 is a = 3 cm, b = 10 cm, h = 8 cm, and l ≈ 2.31 cm.
Please note that these are just two sets of possible dimensions for the given volumes. There can be many other combinations that would result in a volume of 120 cubic centimeters for each trapezoidal prism.