A circular pond is surrounded by a path 2 m wide. If the total area (pond + path) is 616 m² and the pond area is 452.16 m², what is the radius of the pond?

Correct — C. The pond's own area fixes its radius.

πr² = 452.16
r² = 452.16 ÷ 3.14 = 144
r = √144 = 12 m

Cross-check with the total: πR² = 616
R² = 616 × 7⁄22 = 196, so R = 14 m
Pond radius = 14 − 2 = 12 m → option (c)

Why the others are wrong

• (a)
  10 m — 10 m takes the 2 m path off twice. The path narrows the diameter by 4 m but the radius by only 2 m, and a 10 m pond covers just 3.14 × 100 = 314 m².
• (b)
  11 m — 11 m makes the pond 3.14 × 121 = 379.94 m², not 452.16 m². Its outer radius, 13 m, would enclose about 531 m², not 616 m².
• (d)
  13 m — 13 m makes the pond 3.14 × 169 = 530.66 m², more than the 452.16 m² stated. A 15 m outer radius would enclose about 707 m², not 616 m².

A path of width w around a circle of radius r makes a larger, concentric circle of radius r + w. The pond and the pond-plus-path are these two circles.

The stem gives more than you need. The pond's area alone fixes r, and the total area with the 2 m width fixes it again, so you get a built-in check.

Key facts

• A path w wide around a circle of radius r gives an outer radius of r + w.
• 3.14 × 144 = 452.16, so a 452.16 m² circle (π = 3.14) has radius 12 m.
• 22⁄7 × 196 = 616, so a 616 m² circle (π = 22⁄7) has radius 14 m.

Common traps

• Stopping at 14 m, the radius of the pond plus the path
• Subtracting the path's width twice from the radius, which gives 10 m

No directly related past PYQ was found.