Find the area of a quadrant of a circle whose circumference is 22 cm. (Use $\pi = \frac{22}{7}$)

Q: Find the area of a quadrant of a circle whose circumference is 22 cm. (Use $\pi = \frac{22}{7}$)

Given:\nCircumference ($C$) = 22 cm \nStep 1: Find the radius ($r$) of the circle using the circumference formula. $C = 2\pi r$ $22 = 2 \times \frac{22}{7} \times r$ $22 = \frac{44}{7} \times r$ $r = \frac{22 \times 7}{44}$ $r = \frac{7}{2} \text{ cm} = 3.5 \text{ cm}$ \nStep 2: Find the area of the quadrant.\nA quadrant of a circle is a sector with an angle $\theta = 90^{\circ}$.\nArea of quadrant = $\frac{1}{4} \times \pi r^2$\nArea = $\frac{1}{4} \times \frac{22}{7} \times \left(\frac{7}{2}\right)^2$\nArea = $\frac{1}{4} \times \frac{22}{7} \times \frac{49}{4}$\nArea = $\frac{1 \times 22 \times 49}{4 \times 7 \times 4}$\nArea = $\frac{11 \times 7}{4 \times 2}$\nArea = $\frac{77}{8} \text{ cm}^2 = 9.625 \text{ cm}^2$ \nTherefore, the area of the quadrant is $9.625 \text{ cm}^2$ (or $\frac{77}{8} \text{ cm}^2$).

Question

Accepted Answer

Given:
Circumference ($C$) = 22 cm 
Step 1: Find the radius ($r$) of the circle using the circumference formula. $C = 2\pi r$ $22 = 2 	imes \frac{22}{7} 	imes r$ $22 = \frac{44}{7} 	imes r$ $r = \frac{22 	imes 7}{44}$ $r = \frac{7}{2} 	ext{ cm} = 3.5 	ext{ cm}$ 
Step 2: Find the area of the quadrant.
A quadrant of a circle is a sector with an angle $	heta = 90^{\circ}$.
Area of quadrant = $\frac{1}{4} 	imes \pi r^2$
Area = $\frac{1}{4} 	imes \frac{22}{7} 	imes \left(\frac{7}{2}ight)^2$
Area = $\frac{1}{4} 	imes \frac{22}{7} 	imes \frac{49}{4}$
Area = $\frac{1 	imes 22 	imes 49}{4 	imes 7 	imes 4}$
Area = $\frac{11 	imes 7}{4 	imes 2}$
Area = $\frac{77}{8} 	ext{ cm}^2 = 9.625 	ext{ cm}^2$ 
Therefore, the area of the quadrant is $9.625 	ext{ cm}^2$ (or $\frac{77}{8} 	ext{ cm}^2$).

NCERT · Class 10 · Mathematics · Areas Related to CirclesFind the area of a quadrant of a circle whose circumference is 22 cm. (Use $\pi = \frac{22}{7}$)