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Each edge of a cube is increased by $50 \%$. Find the percentage increase in the surface area of the cube.
Given:
Each edge of a cube is increased by $50 \%$.
To do:
We have to find the percentage increase in the surface area of the cube.
Solution:
Let the edge of the cube be $a$.
This implies,
Total surface area $= 6a^2$
The new edge of the cube $=\frac{150 \times a}{100}$
$=\frac{3}{2} a$
New total surface area of the cube $=6(\frac{3}{2} a)^{2}$
$=\frac{6 \times 9}{4} a^{2}$
$=\frac{27}{2} a^{2}$
Increase in surface area $=\frac{27}{2} a^{2}-6 a^{2}$
$=\frac{27-12}{2} a^{2}$
$=\frac{15}{2} a^{2}$
Increase in percent $=\frac{\frac{15 a^{2}}{2}}{6a^2} \times 100$
$=\frac{5 \times 100}{4}$
$=125 \%$
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