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Answer :
To find the difference between the areas of two circles given their diameters, we can follow these steps:
1. Determine the Radius of Each Circle:
- The diameter of the first circle is 12 centimeters. The radius is half of the diameter:
[tex]\[
\text{Radius of Circle 1} = \frac{12}{2} = 6 \text{ centimeters}
\][/tex]
- The diameter of the second circle is 9 centimeters. The radius is:
[tex]\[
\text{Radius of Circle 2} = \frac{9}{2} = 4.5 \text{ centimeters}
\][/tex]
2. Calculate the Area of Each Circle:
- Use the formula for the area of a circle, which is [tex]\( \pi \times \text{radius}^2 \)[/tex].
- For the first circle:
[tex]\[
\text{Area of Circle 1} = \pi \times (6)^2 = \pi \times 36
\][/tex]
- For the second circle:
[tex]\[
\text{Area of Circle 2} = \pi \times (4.5)^2 = \pi \times 20.25
\][/tex]
3. Find the Difference in Areas:
- Subtract the area of the second circle from the area of the first circle:
[tex]\[
\text{Difference in Areas} = \pi \times 36 - \pi \times 20.25
\][/tex]
- Simplify by factoring out [tex]\( \pi \)[/tex]:
[tex]\[
\text{Difference in Areas} = \pi \times (36 - 20.25) = \pi \times 15.75
\][/tex]
4. Estimate the Final Answer:
- Calculate this value and round it to the nearest whole number.
- The closest estimation for the difference in the areas is 49 square centimeters.
Therefore, the most accurate estimation of the difference in areas of the two circles is 49 square centimeters.
1. Determine the Radius of Each Circle:
- The diameter of the first circle is 12 centimeters. The radius is half of the diameter:
[tex]\[
\text{Radius of Circle 1} = \frac{12}{2} = 6 \text{ centimeters}
\][/tex]
- The diameter of the second circle is 9 centimeters. The radius is:
[tex]\[
\text{Radius of Circle 2} = \frac{9}{2} = 4.5 \text{ centimeters}
\][/tex]
2. Calculate the Area of Each Circle:
- Use the formula for the area of a circle, which is [tex]\( \pi \times \text{radius}^2 \)[/tex].
- For the first circle:
[tex]\[
\text{Area of Circle 1} = \pi \times (6)^2 = \pi \times 36
\][/tex]
- For the second circle:
[tex]\[
\text{Area of Circle 2} = \pi \times (4.5)^2 = \pi \times 20.25
\][/tex]
3. Find the Difference in Areas:
- Subtract the area of the second circle from the area of the first circle:
[tex]\[
\text{Difference in Areas} = \pi \times 36 - \pi \times 20.25
\][/tex]
- Simplify by factoring out [tex]\( \pi \)[/tex]:
[tex]\[
\text{Difference in Areas} = \pi \times (36 - 20.25) = \pi \times 15.75
\][/tex]
4. Estimate the Final Answer:
- Calculate this value and round it to the nearest whole number.
- The closest estimation for the difference in the areas is 49 square centimeters.
Therefore, the most accurate estimation of the difference in areas of the two circles is 49 square centimeters.
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