Question

During cold working, a metal experiences a 10\% reduction in cross-sectional area. If the original cross-sectional area was 1 cm\(^2\), what is the new cross-sectional area?

• A. 0.90 cm\(^2\)
• B. 0.95 cm\(^2\)
• C. 0.10 cm\(^2\)
• D. (1)10 cm\(^2\)

Hint:

Percentage Reduction. Reduction of X% means the final value is (100-X)% of the original value. Final = Original \(\times\) (1 - Percentage Reduction/100).

Answer 1

The Correct Option is A

Cold working involves deforming a metal below its recrystallization temperature.
A reduction in cross-sectional area means the area decreases.
Original Area (\(A_0\)) = 1 cm\(^2\).
Percentage Reduction in Area = 10%.
Amount of Reduction = 10% of \(A_0\) = 0.
10 \(\times\) 1 cm\(^2\) = 0.
10 cm\(^2\).
New Area (\(A_f\)) = Original Area - Amount of Reduction $$ A_f = A_0 - 0.
10 A_0 = A_0 (1 - 0.
10) $$ $$ A_f = 1 \, \text{cm}^2 - 0.
10 \, \text{cm}^2 = 0.
90 \, \text{cm}^2 $$ The new cross-sectional area is 0.
90 cm\(^2\).