Question

Two circular ponds have circumferences in the ratio 3:5. If the smaller pond has an area of 150 m², what is the approximate area of the larger pond?

• A. 417 m²
• B. 528 m²
• C. 450 m²
• D. 438 m²

Answer 1

Answer:

A. 417 m²

Circumference (C = 2\pi r), so circumference is directly proportional to radius.

Ratio of radii

Given:
$C_1 : C_2 = 3 : 5$

So,
$r_1 : r_2 = 3 : 5$

Step 2: Ratio of areas

Area of circle $(A \propto r^2)$

$A_1 : A_2 = 3^2 : 5^2 = 9 : 25$

Use given area

Smaller pond area = 150 m² corresponds to 9 parts.

So,
$9 \text{ parts} = 150$
$1 \text{ part} = \frac{150}{9} = 16.67$
Find larger area

$25 \text{ parts} = 25 \times 16.67 \approx 416.75$

Final Answer:

$\boxed{\approx 417 \text{ m}^2}$