Question

The area of a circle with a circumference of 220 cm is equal to the area of a rectangle. The width of the rectangle is 50 cm. Which of the following statement/statements are correct?

1. The radius of the circle is 70 cm.

2. The length of the rectangle is 77 cm.

• A. 1 ഉം 2 ഉം തെറ്റാണ്
• B. 1 തെറ്റും 2 ശരിയും ആണ്
• C. 1 ശരിയും 2 തെറ്റും ആണ്
• D. 1 ഉം 2 ഉം ശരിയാണ്

Answer 1

Answer:

B. 1 തെറ്റും 2 ശരിയും ആണ്

The only correct statement is "The length of the rectangle is $77\text{ cm}$."

1. Find the radius of the circle

The circumference of a circle is given by $C = 2\pi r$.

• $220 = 2 \times \frac{22}{7} \times r$

• $220 = \frac{44}{7} \times r$

• $r = \frac{220 \times 7}{44} = 5 \times 7 = \mathbf{35\text{ cm}}$

• Statement 1 is incorrect (Radius is $35\text{ cm}$, not $70\text{ cm}$).

2. Find the area of the circle

The area of a circle is given by $A = \pi r^2$.

• $A = \frac{22}{7} \times 35 \times 35$

• $A = 22 \times 5 \times 35$

• $A = \mathbf{3850\text{ cm}^2}$

3. Find the length of the rectangle

The area of the rectangle is equal to the area of the circle ($3850\text{ cm}^2$).
The formula for the area of a rectangle is $A = \text{length} \times \text{width}$.

• $3850 = \text{length} \times 50$

• $\text{length} = \frac{3850}{50}$

• $\text{length} = \mathbf{77\text{ cm}}$

• Statement 2 is correct.

Final Answer

The correct statement is: The length of the rectangle is $77\text{ cm}$.