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3 years ago

Can someone help me with this? Thank you :)

Mathematics

1 answer:

aivan3 [116]3 years ago

6 0

Answer: The area of the shaded region is 150.72 km^2

Step-by-step explanation: The first bit of information we have is that both the inner circle and the outer circle have the same center. The radius of the inner circle can be calculated since we have been given the circumference (25.12) and the value of pi (3.14). The circumference of a circle is given as

Circumference = 2 x Pi x radius

With the values available, we now have

25.12 = 2 x 3.14 x radius

25.12 = 6.28 x radius

Divide both sides of the equation by 6.28

radius = 4

Having calculated the radius of the inner circle, the area now becomes;

Area = Pi x radius^2

Area = 3.14 x 4^2

Area = 3.14 x 16

Area = 50.24 km^2

The radius of the outer circle is the addition of 4 (on the shaded region) to the radius of the inner circle and that gives us 8.

Next we calculate the area of the outer circle which is

Area = Pi x radius^2

Area = 3.14 x 8^2

Area = 3.14 x 64

Area = 200.96 km^2

Now that we have determined the area of both the inner circle and the outer circle, the area of the shaded region is simply the difference between both of them, that is

Area of shaded region = 200.96 - 50.24

= 150.72 km^2

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Given

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Required

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$cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}$

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Rationalize the denominator

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}$

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