# What is the Percentage Increase in the Total Surface Area? if

Each edge of a cube is increased by 25 %. Find the percentage increase in the total surface area:

- 25%
- 56.25%
- 55.25%
- 16.84%

**Answer: (2) 56.25 %**

**Explanation:-**

Let the edge of a surface area = a

**Formula-**

**The surface area of a cube = 6a ^{2}**

**Where, a = edge of a cube.**

Then, the surface area of a cube = 6a

^{2}

If edge increased by 25 %,

Then , the surface area of a cube = 6 (a + a 25/100)^{2}

= 6 (a + a/4)^{2}

= 6 (5a/4)^{2}

= 6 x 5 a x 5 a /4 x 4

= 75 a^{2}/8

Increased surface area = 75 a^{2}/8 – 6 a^{2}

= (75 a^{2} – 48 a^{2})/8

= 27 a^{2}/8

Percentage of increased area = 27 a^{2} x 100/8 x 6 a^{2}

= 9 x 25/2 x 2

= 225/4

= 56.25 %

Then, the increased surface area is 56.25 %.

Hence, the answer answer is (2) 56.25%.