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icang [17]
3 years ago
9

An igloo is a shelter constructed from blocks of ice in the shape of a hemisphere. This igloo has an entrance below ground level

. The outside diameter of the igloo is 12 feet. The thickness of each block of ice that was used to construct the igloo is 1.5 feet. Estimate in cubic feet the amount of space of the living area inside the igloo
Mathematics
1 answer:
Sloan [31]3 years ago
4 0
The living area inside would be 190.755 ft³.

We find the volume inside the hemisphere.  The volume of a sphere is given by the formula
V = (4/3)πr³

Since this is a hemisphere, it is half of the volume:
V = 1/2(4/3)πr³ = 4/6πr³ = 2/3πr³

The diameter of the hemisphere is 12 ft.  However, there is 1.5 ft on each side that is a solid block of ice and not living space:
12 - 2(1.5) = 12-3 = 9 ft for the diameter.

The radius is half of the diameter:
9/2 = 4.5

Using this, we have 
V = 2/3πr³ = 2/3(3.14)(4.5)³ = 190.755 ft³
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Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean $ \pm $ Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 = $ \frac{68}{100} \times 1200 $

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean $ \pm $ 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to $ \frac{95}{2} \% $ of the values.

Therefore, Scores between 72 and 90 = $ \frac{95}{2(100)} \times 1200 = \frac{95}{200} \times 1200  $

$ \implies 95 \times 12 $ = 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 = $ \frac{2.5}{100} \times 1200 $

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

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