Solution Procedure
Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:
... C = 2√(πA)
To find ten times this circumference, we calculate:
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
Derivation of Formulas
The standard formulas for circumference and area are:
... C = 2πr
... A = πr²
Multiplying the area formula by π and extracting the square root yields:
... πA = (πr)²
... √(πA) = πr
Doubling this value results in the circumference formula:
... C = 2√(πA) = 2πr
$125,060,000
one-hundred twenty-five million, and sixty thousand dollars
Also, 125.06 expressed as a fraction is 6253/50, if that representation is acceptable.
You can refer to it as 125.06 million dollars when using the figure from the prompt.
<span>With AB tangent at D, where AD = OD = 4
, triangle OAD forms a right angle with sides measuring 4 and 4.
So, the area of triangle OAD is computed as 1/2 * 4 * 4 = 8
The angles AOD and DAO equal 45 degrees.
Therefore, the area of circular sector OCD is calculated as the area of circle O multiplied by 45/360
= pi * 4 * 4 * 45/360
= 2pi
The shaded area ACD results from the triangle OAD minus the area of circular sector OCD
= 8 - 2pi
= 1.72
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