if each edge of a cube is increased by25 then the percentange..., Area & Volume, General Mathematics

Question:If each edge of a cube is increased by`25%` then the percentange increase in its surface area is :

A `25%` 
B `50%` 
C `48.75%` 
D `56.25%`

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+ AnswerD

+ ExplanationLet original edge = a. Then, surface area`= 6a^2`

New edge`= 125/100 a = (5a/4).`

New surface area

`= 6 xx ((5a)/(4))^2`

`= (75a^2)/8.`

Increase in surface area

`= ((75a^2)/(8) - 6a^2)`

`= (27a^2)/8.`

Increase`% = ((27a^2)/8 xx 1/(6a^2) xx 100)%`

`= 56.25%.`

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