Question

If Edge of a cube is increased by 25%,Find the percentage increase in the surface area!

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Answer 1

hey friend
here is ur answer
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Answer 2

Answer:

1.56%

Step-by-step explanation:

$\text{Let the previous edge be x units.}\\\\\text{After 25 \% increase, edge = x + (25 \% of x)}\\\\= x + \dfrac{25}{100} \times x\\\\\\= x + \dfrac{x}{4}\\\\\\= \dfrac{4x+x}{4}\\\\\\= \dfrac{5x}{4} \: units\\\\\\\text{Total Surface Area of cube having edge x units = 6(x)}^2 = 6x^2 \: unit^2\\\\\text{Now, Total surface area of cube having edge \dfrac{5}{4}x units}\\\\= 6 \times (\dfrac{5}{4} \times x)^2\\\\\\= \dfrac{6 \times 25 \times x^2}{16}$

$= \dfrac{75x^2}{8} \: unit^2\\\\\\\text{Now, \% increase in TSA = } \dfrac{\text{TSA of cube with edge \dfrac{5}{4}x units}}{\text{TSA of cube with edge x units}} \times 100\\\\\\= \dfrac{75x^2}{8} \div 6x^2\\\\\\= \dfrac{75x^2 \times 1}{8 \times 6x^2}\\\\\\= \dfrac{75}{48}\\\\\\= \large \underline{\boxd{\boxed{\boxed{\mathsf{1.56 \%}}}}}$

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