Geometry

Solids

Medium

If each side of a cube is decreased by $19 \%$ , then the decrease in surface area is :

$40 \%$

$34.39 \%$

$38.4 \%$

$19 \%$

✅ Correct Option: 2

Let original side length be $s$

New side length $= s(1-0.19) = 0.81s$

Original surface area $(SA_1)$ :

$SA_1 = 6s^2$

New surface area $(SA_2)$ :

$SA_2 = 6(0.81s)^2$

$SA_2 = 6(0.6561s^2)$

$SA_2 = 0.6561(6s^2)$

$SA_2 = 0.6561SA_1$

Decrease in surface area $= SA_1 - SA_2$

$= SA_1 - 0.6561SA_1$

$= SA_1(1 - 0.6561)$

$= SA_1(0.3439)$

$= 34.39\%$ of original surface area.

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If each side of a cube is decreased by $19 \%$ , then the decrease in surface area is :