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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Updated on: 10-Oct-2022

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