(a) $$ 1: 16 $$ (b) $$ 1: 32 $$ The area of a quadrant of a circle whos circumference is 22 cm is

Question

UpStudy AI · Accepted Answer

To find the area of a quadrant of a circle with a circumference of 22 cm, follow these steps:

### Step 1: Calculate the Radius
The formula for the circumference $$ C $$ of a circle is:
$$ C = 2\pi r $$
Given $$ C = 22 $$ cm, solve for $$ r $$:
$$ 22 = 2\pi r $$
$$ r = \frac{22}{2\pi} $$
$$ r = \frac{11}{\pi} \text{ cm} $$

### Step 2: Calculate the Area of the Full Circle
The area $$ A $$ of a full circle is:
$$ A = \pi r^2 $$
Substitute $$ r = \frac{11}{\pi} $$:
$$ A = \pi \left( \frac{11}{\pi} \right)^2 $$
$$ A = \pi \left( \frac{121}{\pi^2} \right) $$
$$ A = \frac{121}{\pi} \text{ cm}^2 $$

### Step 3: Calculate the Area of the Quadrant
A quadrant is one-fourth of a circle. Therefore:
$$ \text{Area of Quadrant} = \frac{1}{4} \times \frac{121}{\pi} $$
$$ \text{Area of Quadrant} = \frac{121}{4\pi} \text{ cm}^2 $$

### Step 4: Numerical Approximation (Optional)
If you prefer a numerical value:
$$ \text{Area of Quadrant} \approx \frac{121}{4 \times 3.1416} $$
$$ \text{Area of Quadrant} \approx \frac{121}{12.5664} $$
$$ \text{Area of Quadrant} \approx 9.63 \text{ cm}^2 $$

**Final Answer:**
The area of the quadrant is $$ \frac{121}{4\pi} $$ cm², which is approximately **9.63 cm²**.
The area of the quadrant is $$ \frac{121}{4\pi} $$ cm², which is approximately **9.63 cm²**.

(a)
(b)
The area of a quadrant of a circle whos
circumference is 22 cm is

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Solución

Step 1: Calculate the Radius

Step 2: Calculate the Area of the Full Circle

Step 3: Calculate the Area of the Quadrant

Step 4: Numerical Approximation (Optional)

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(a) (b) The area of a quadrant of a circle whos circumference is 22 cm is