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igomit [66]
3 years ago
7

A circle with radius of \greenD{6\,\text{cm}}6cmstart color #1fab54, 6, start text, c, m, end text, end color #1fab54 sits insid

e a circle with radius of \blueD{9\,\text{cm}}9cmstart color #11accd, 9, start text, c, m, end text, end color #11accd.
What is the area of the shaded region?

Round your final answer to the nearest hundredth

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
3 0

Answer: 141 cm^{2}

Step-by-step explanation:

We have two circles:

Cirlce 1, with a radius r=6 cm and area A_{1}:

A_{1}=\pi r^{2}

And Cicle 2, with a radius R=9 cm and area A_{2}:

A_{1}=\pi R^{2}

Since Circle 1 is inside Circle 2 and assuming the area of the shaded region is the shown in the attached image, its area is:

A=A_{2}-A_{1}=\pi R^{2}-\pi r^{2}

A=\pi (R^{2}- r^{2})

A=\pi ((9cm)^{2}- (6cm)^{2})

Finally:

A=141.37 cm^{2} \approx 141 cm^{2}

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