JIPMAT 2024 (QA) - If each side of a cube is decreased by 19 \%, then the decrease in surface area is : | PYQs + Solutions | AfterBoards
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JIPMAT 2024

Geometry
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Solids

Medium

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

Correct Option: 2
Let original side length be ss \newline \newline New side length =s(1−0.19)=0.81s= s(1-0.19) = 0.81s \newline \newline
\newline Original surface area (SA1)(SA_1): \newline \newline SA1=6s2SA_1 = 6s^2 \newline \newline New surface area (SA2)(SA_2): \newline \newline SA2=6(0.81s)2SA_2 = 6(0.81s)^2 \newline \newline SA2=6(0.6561s2)SA_2 = 6(0.6561s^2) \newline \newline SA2=0.6561(6s2)SA_2 = 0.6561(6s^2) \newline \newline SA2=0.6561SA1SA_2 = 0.6561SA_1 \newline \newline
\newline Decrease in surface area =SA1−SA2= SA_1 - SA_2 \newline \newline =SA1−0.6561SA1= SA_1 - 0.6561SA_1 \newline \newline =SA1(1−0.6561)= SA_1(1 - 0.6561) \newline \newline =SA1(0.3439)= SA_1(0.3439)
\newline =34.39%= 34.39\% of original surface area.

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