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2 answers:
Answer:
The surface area of the prism is 276 in.²
If you are also looking for the volume of the prism, it is 280.
Step-by-step explanation:
It's hard to find the surface area and the volume of the prism if you're just looking at the net of the 3D shape. There are some unnecessary measurements that will definitely throw you off. I drew a sample prism so it's easier to solve. Check the linked image.
The formula in finding the surface area of a prism is SA = 2(wl + hl + hw), where w is for width, l is for length, and h is for height. The point of all of these calculations is to find the area of 3 different faces of the prism and then you add up all of the areas and multiply the sum by 2 to give you the surface area. Looks a lot but it's worth getting the answer right.
The formula in finding the volume of the prism is V = w * h * l, where w is for width, h is for height, and l is for length. Simple multiplication of 3 different sides and you'll get the volume. I hope this helps and if I am wrong please let me know! :D
Answers:
- Surface Area = 276 square inches
- Volume = 280 cubic inches
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Explanation:
It might help to draw this out on paper, cut the figure out, and fold along the lines to form a 3D box.
Check out the diagram below. In steps 1 through 4, we go from a flat 2D net to a 3D box. Steps 2 and 3 basically are just intermediate steps to show the folding process. If this was done with an animation, it might look better (you'll have to use your imagination a bit).
The letters A through F in red should help us see how the flat 2D figure connects to the 3D one. For me, it helps to picture a room. The floor is face B, the ceiling is E, and so on.
Anyways, once we get the 3D box, it has the following dimensions:
- L = length = 10 inches
- W = width = 7 inches
- H = height = 4 inches
The order of length, width and height doesn't matter.
Once we know these values, we can plug them into the formulas below
- SA = 2(LW+LH+WH)
- V = LWH
where SA and V are the surface area and volume respectively.
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So,
SA = 2(LW+LH+WH)
SA = 2(10*7 + 10*4 + 7*4)
SA = 2*(70+40+28)
SA = 2*138
SA = 276 square inches is the surface area
and,
V = L*W*H
V = 10*7*4
V = 280 cubic inches is the volume
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As an alternative way to get the surface area, you can compute the areas of rectangles A through F, and then add up those areas to get the overall surface area.
It's a bit interesting how the surface area and volume are almost nearly the same number. Though that could be a coincidence.
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Answer:
If we compare the p value and the significance level given for example we see that
so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.
Step-by-step explanation:
1) Data given and notation
represent the sample mean
represent the standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Calculate the P-value
First we find the degrees of freedom:
Since is a one-side upper test the p value would be:
Conclusion
If we compare the p value and the significance level given for example we see that
so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.