Question
The radius is 5.5 feet.
) The area of the whole circle is A = (5.5)squared π .
The area of the whole circle is A = (11) squared π.
) The area of the shaded region can be found by multiplying the area of the whole circle by three-fourths as in
A= π (r squared).
) The area of the shaded region can be found by multiplying the area of the whole circle by two-thirds as in
A= π(r squared)
) The area of the whole circle is A = (5.5)squared π .
The area of the whole circle is A = (11) squared π.
) The area of the shaded region can be found by multiplying the area of the whole circle by three-fourths as in
A= π (r squared).
) The area of the shaded region can be found by multiplying the area of the whole circle by two-thirds as in
A= π(r squared)
Answers
Answered by
GPT-4o mini
Let's clarify the relationships presented in your statements and calculate the correct areas step by step.
1. **Area of the Whole Circle**:
The formula for the area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle. Given that the radius is \( 5.5 \) feet, the area can be calculated as follows:
\[
A = \pi (5.5)^2 = \pi (30.25) \approx 95.03 \text{ square feet} \quad (\text{using } \pi \approx 3.14)
\]
2. **Correct Calculation Parameters**:
Your mention of \( A = (11)^2 \pi \) seems to suggest a diameter of \( 11 \) feet, which comes from doubling the radius. However, this would not apply to the area calculated directly from the radius. The correct area of the whole circle is derived from the radius, as shown above, not the diameter.
3. **Area of the Shaded Region**:
- If we want to find the area of a shaded region that is a fraction of the whole circle's area, we need to use a multiplier.
- If you assume three-fourths of the area is shaded, the area of the shaded region would be:
\[
\text{Area of shaded region} = \frac{3}{4} A = \frac{3}{4} \left( \pi (5.5)^2 \right) = \frac{3}{4} \left( \pi (30.25) \right) \approx 71.27 \text{ square feet}
\]
- Similarly, if you are told that two-thirds of the area is shaded, the calculation would be:
\[
\text{Area of shaded region} = \frac{2}{3} A = \frac{2}{3} \left( \pi (5.5)^2 \right) \approx 63.35 \text{ square feet}
\]
In summary, you can determine the area of a shaded region by using the area of the whole circle and multiplying it by the appropriate fraction (either \(\frac{3}{4}\) or \(\frac{2}{3}\), depending on the context given). Always start with the correct area formula \( A = \pi r^2 \) based on the given radius.
1. **Area of the Whole Circle**:
The formula for the area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle. Given that the radius is \( 5.5 \) feet, the area can be calculated as follows:
\[
A = \pi (5.5)^2 = \pi (30.25) \approx 95.03 \text{ square feet} \quad (\text{using } \pi \approx 3.14)
\]
2. **Correct Calculation Parameters**:
Your mention of \( A = (11)^2 \pi \) seems to suggest a diameter of \( 11 \) feet, which comes from doubling the radius. However, this would not apply to the area calculated directly from the radius. The correct area of the whole circle is derived from the radius, as shown above, not the diameter.
3. **Area of the Shaded Region**:
- If we want to find the area of a shaded region that is a fraction of the whole circle's area, we need to use a multiplier.
- If you assume three-fourths of the area is shaded, the area of the shaded region would be:
\[
\text{Area of shaded region} = \frac{3}{4} A = \frac{3}{4} \left( \pi (5.5)^2 \right) = \frac{3}{4} \left( \pi (30.25) \right) \approx 71.27 \text{ square feet}
\]
- Similarly, if you are told that two-thirds of the area is shaded, the calculation would be:
\[
\text{Area of shaded region} = \frac{2}{3} A = \frac{2}{3} \left( \pi (5.5)^2 \right) \approx 63.35 \text{ square feet}
\]
In summary, you can determine the area of a shaded region by using the area of the whole circle and multiplying it by the appropriate fraction (either \(\frac{3}{4}\) or \(\frac{2}{3}\), depending on the context given). Always start with the correct area formula \( A = \pi r^2 \) based on the given radius.