Question

The length of a wire which is tied as a boundary of a semicircular park is 72 m. Find the radius of the semi-circular park and its area. [Hint: (πr + 2r) = 72]

Answer 1

Given:

Length of wire (boundary of semicircular park) = 72 m.

The boundary length = semicircular arc + diameter = πr + 2r (hint).

Step-wise calculation:

1. Form equation:

πr + 2r

= 72r (π + 2) 

= 72

2. Solve for r (exact form): 

r = `72/(π + 2)` metres

Numeric approximation (Use π = 3.1415926536):

π + 2 = 5.1415926536

r = `72/5.1415926536`

= 14.0034 m   ...(Rounded r = 14.003 m = 14.00 m)

3. Area of the semicircle:

A = `1/2 πr^2`

= `π/2 xx [72/(π + 2)]^2`   ...(Exact form)

Numeric: r² = (14.0034)² 

= 196.0964 

A = 0.5 × π × 196.0964

= 308.03 m²

Radius r = `72/(π + 2)`

= 14.003 m   ...(≈ 14.00 m)

Area of the semicircular park = 308.03 m².