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AveGali [126]
3 years ago
5

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 fee

t. Estimate in cubic feet the amount of space of the living area inside the igloo.
Mathematics
1 answer:
mojhsa [17]3 years ago
6 0
The first thing we are going to do for this case is to model the igloo as a hemisphere.
 The volume of the hemisphere is:
 V = ((4/3) * (pi) * (r ^ 3)) / 2
 Where,
 r: sphere radio
 We have then that the internal diameter is:
 di = 12-1.5
 di = 10.5 feet
 So the radio is:
 r = di / 2
 r = 10.5 / 2
 r = 5.25 feet
 Substituting values:
 V = ((4/3) * (pi) * ((5.25) ^ 3)) / 2
 V = 303.1 feet ^ 3
 Answer:
 
the amount of space of the living area inside the igloo is:
 
V = 303.1 feet ^ 3
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First, let's look at the identities:

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The question asks to find sin(A - B); therefore, we need to use the difference identity.

Based on the given information (value and quadrant), we can draw reference triangles to find the simplified values of A and B.

sin(A) = \frac{24}{25}

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Plug these values into the difference identity formula.

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sin(A - B) = (\frac{24}{25})(\frac{3}{5}) - (-\frac{4}{5})(\frac{7}{25})

Multiply.

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Add.

sin(A - B) = \frac{4}{5}

This is your answer.

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