Each edge of a cube is increases by 50%. Find the percentage increase

1.	Each edge of a cube is increases by 50%. Find the percentage increase in the surface of area of the cube.
Answer» Given, Increment in each edge = 50% Let edge of cube = a So surface area of cube = a² (after 50% increase ) Length of edge of cube = a + a\(\times\cfrac{50}{100}\) = \(a+\cfrac{a}2=\cfrac{3a}2\) Surface area of cube = \(\Big(\cfrac{3a}{2}\Big)^2=\cfrac{9a^2}{4}\) Increment in area = \(\cfrac{9a^2}{4}-a^2=\cfrac{5a^2}{4}\) % increment = \(\cfrac{(increased\,area)}{original\,area}\) = \(\cfrac{\frac{5a^2}{4}}{a^2}\times100\) = 125%

Each edge of a cube is increases by 50%. Find the percentage increase in the surface of area of the cube.

Answer»

Given,

Increment in each edge = 50%

Let edge of cube = a

So surface area of cube = a²

(after 50% increase )

Length of edge of cube = a + a\(\times\cfrac{50}{100}\) = \(a+\cfrac{a}2=\cfrac{3a}2\)

Surface area of cube = \(\Big(\cfrac{3a}{2}\Big)^2=\cfrac{9a^2}{4}\)

Increment in area = \(\cfrac{9a^2}{4}-a^2=\cfrac{5a^2}{4}\)

% increment = \(\cfrac{(increased\,area)}{original\,area}\) = \(\cfrac{\frac{5a^2}{4}}{a^2}\times100\)

= 125%