✒️AREA
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[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]
- Find the area of a shaded region of each circle has diameter of 20cm
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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]
[tex] \qquad \Large \:\: \rm{\approx 172 \: sq. \: cm.} [/tex]
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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
- To find the area of the shaded region, we must subtract the area of the two inscribed circles from the area of the rectangle.
» Since the circles have a diameter of 20cm, then the rectangle's dimensions are 40cm and 20cm. Find the area of the rectangle.
[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm Area = l \cdot w} \end{align} [/tex]
- [tex] Area = 40 \cdot 20 \: cm^2 [/tex]
- [tex] Area = 800 \: cm^2 [/tex]
» Find the area of one of the circles. Since the diameter is 20cm, then its radius is 10cm.
[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm Area = \pi r^2} \end{align} [/tex]
- [tex] Area = \pi (10)^2 \:cm^2 [/tex]
- [tex] Area = 100\pi \:cm^2 [/tex]
» Multiply the area by two since there are two of them.
- [tex] Area = 2(100\pi) \:cm^2 [/tex]
- [tex] Area = 200\pi \:cm^2 [/tex]
» Let 3.14 be the approximate value of pi.
- [tex] Area \approx 200(3.14) \:cm^2 [/tex]
- [tex] Area \approx 628 \:cm^2 [/tex]
» Find the area of the shaded (orange) region.
- [tex] Area \approx 800 \:cm^2 - 628 \: cm^2 [/tex]
- [tex] Area \approx 172 \: cm^2 [/tex]
[tex] \therefore [/tex] The area of the shaded region is about 172 sq. centimeters
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