If each edge of a cube is increased by 50%, the percentage increase in the surface area is

Question:

If each edge of a cube is increased by 50%, the percentage increase in the surface area is
(a) 50%
(b) 75%
(c) 100%
(d) 125%

Solution:

(d) 125%
Let the original edge of the cube be a units.
Then, the original surface area of the cube = 6a2 units

New edge of the cube = 150% of a

$=\frac{150 a}{100}$

$=\frac{3 a}{2}$

Hence, new surface area $=6 \times\left(\frac{3 a}{2}\right)^{2}$

$=\frac{27 a^{2}}{2}$

Increase in area $=\left(\frac{27 a^{2}}{2}-6 a^{2}\right)$

$=\frac{15 a^{2}}{2}$

$\%$ increase in surface area $=\left(\frac{15 a^{2}}{2} \times \frac{1}{6 a^{2}} \times 100\right) \%$

$=125 \%$

 

 

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