A circular walking track with a uniform width of 2m is constructed along the outer edge of a round garden having a radius of 10m. What is the total surface area covered by the track?

The correct option is 138.2 m².

Understanding the Problem:
A circular walking track built around a circular garden forms a ring-shaped geometric region known as an annulus. To calculate the total surface area covered by this track, we subtract the surface area of the inner circular garden from the surface area of the larger outer circle (garden + track).

Given Data:
Inner radius of the garden (r) = 10 m
Uniform width of the walking track (w) = 2 m

Step 1: Determine the Outer Radius (R)
The outer radius is equal to the inner radius plus the width of the track.

$R=r+w=10\text{m}+2\text{m}=12\text{m}$

Step 2: Formula for the Area of the Circular Track
The area of the track is given by the difference between the areas of the outer and inner circles:

$\text{Area of Track}=\pi R^2-\pi r^2=\pi (R^2-r^2)$

Step 3: Calculate the Area
Substitute the values of outer radius (R = 12 m) and inner radius (r = 10 m) into the formula:

$R^2-r^2={12}^2-{10}^2=144-100=44$

Now, multiply by the value of π (using π ≈ 3.14159):

$\text{Area of Track}=44\times \pi$

$\text{Area of Track}=44\times 3.14159\approx 138.23{\text{m}}^2$

Rounding off to one decimal place, we get 138.2 m².