A uniform wire of length l and radius r has a resistance of 100Ω. It is recast into a wire of radius r/2. The resistance of the new wire will be:

Uniform wire length l
Radius r
Resistance 100Ω
If its radius = r/2
→ r₂/r₁ = l₂/l₁
Area remains constant → l × πr² = l × π(r/2)²
We know, R = ρl/A → R ∝ l/r²
Let R₁ = 100Ω, r₁ = r, l₁ = l
R₂ = ?, r₂ = r/2, l₂ = ?
Volume remains constant → l₁ × πr₁² = l₂ × πr₂²
→ l × πr² = l₂ × π(r/2)²
→ l₂ = 4l
R₁/R₂ = (l₁/r₁²)/(l₂/r₂²) = (l₁/l₂) × (r₂²/r₁²) = (l/4l) × ((r/2)²/r²) = (1/4) × (1/4) = 1/16
→ R₂ = 16R₁ = 16 × 100Ω = 1600Ω