Answer:
49/100
Step-by-step explanation:
So you can find the area of shaded area by finding the area of the circle inside the entire circle that has a diameter of 3 cm and 4 cm and then find the area of the most inner circle which only has a diameter of 4 cm and then subtract these 2. After that you want to find the area of the entire circle and then divide the area of the shaded area by the entire circle. The formula for the area of a circle is given as: [tex]\pi r^2[/tex]
Area of the two "inner" circles of a diameter of 4 and 3 cm. This gives you an entire diameter of 7 cm with a radius of 3.5. The area of this circle is [tex]\pi(3.5)^2[/tex] which is [tex]12.25\pi[/tex].
The area of the most inner circle only has a diameter only 4 cm. The radius is 2, thus the area of this circle is [tex]\pi (2)^2[/tex] which is [tex]4\pi[/tex]. Now subtract this from the 12.25 pi to find the area of the shaded area. This gives you the equation: [tex]12.25\pi-4\pi[/tex] which equals [tex]8.25\pi[/tex].
Now to find the area of the entire circle you add up all the "diameters" which gives you 4 cm + 3 cm + 3 cm = 10 cm. So the radius is 5. This gives you the equation: [tex]\pi(5)^2[/tex] which is equal to [tex]25\pi[/tex].
Now to find the fraction of circle that is shaded we divide the area of the shaded area and the area of the entire circle. This gives you the equation: [tex]\frac{12.25\pi}{25\pi}[/tex] but since it wants it as a fraction, I'm assuming it wants integers in the decimal and numerator place. So we can represent 12.25 as 12 + 1/4. And then convert the 12 into 1/4ths by multiplying by 4 and then adding that to the numerator. This makes the fraction [tex]\frac{49}{4}=12.25[/tex]. So now all we have to is divide the two values: [tex]\frac{\frac{49}{4}}{\frac{25}{1}}[/tex]. If you're wondering where the pi's when you can just cancel them out since they're both in the numerator and denominator. Now all we have to do is keep the 49/4, change the operator to multiplication, and flip the 25/1 to 1/25. This gives you the equation: [tex]\frac{49}{4} * \frac{1}{25}[/tex] which becomes [tex]\frac{49}{100}[/tex] which is the answer
