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each edge of a cube is increased by 20% . what is the percentage increase in the surface area of the cube?
Asked by araima2001 | 18 Jan, 2015, 11:18: AM
answered-by-expert Expert Answer
L e t space apostrophe a apostrophe space b e space t h e space e d g e space o f space t h e space c u b e. space 20 % o f space a equals 20 over 100 cross times a equals a over 5 S i n c e space 20 % space o f space t h e space e d g e space o f space t h e space c u b e space i s space i n c r e a s e d comma space w e space h a v e comma t h e space n e w space e d g e space o f space t h e space c u b e equals a plus a over 5 equals fraction numerator 5 a plus a over denominator 5 end fraction equals fraction numerator 6 a over denominator 5 end fraction space u n i t s S u r f a c e space a r e a space o f space t h e space c u b e space w i t h space e d g e space a equals 6 cross times a squared space s q u a r e space u n i t s S u r f a c e space a r e a space o f space t h e space n e w space c u b e space w i t h space e d g e comma space apostrophe fraction numerator 6 a over denominator 5 end fraction apostrophe space equals 6 cross times open parentheses fraction numerator 6 a over denominator 5 end fraction close parentheses squared space s q u a r e space u n i t s C h a n g e space i n space s u r f a c e space a r e a equals 6 cross times open parentheses fraction numerator 6 a over denominator 5 end fraction close parentheses squared minus 6 cross times a squared equals 6 open square brackets open parentheses fraction numerator 6 a over denominator 5 end fraction close parentheses squared minus a squared close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 6 open square brackets fraction numerator 36 a squared over denominator 25 end fraction minus a squared close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 6 open square brackets fraction numerator 36 a squared minus 25 a squared over denominator 25 end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 6 open square brackets fraction numerator 11 a squared over denominator 25 end fraction close square brackets T h u s space t h e space p e r c e n t a g e space i n c r e a s e space i n space t h e space s u r f a c e space a r e a equals fraction numerator 6 open square brackets fraction numerator 11 a squared over denominator 25 end fraction close square brackets over denominator 6 a squared end fraction cross times 100 equals 44 %
Answered by Vimala Ramamurthy | 18 Jan, 2015, 02:13: PM

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