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:

  1. 25%
  2. 56.25%
  3. 55.25%
  4. 16.84%
Abdul Salam Newbie Asked on 7th August 2015 in Maths.
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1 Answer(s)

Answer: (2) 56.25 %

Explanation:-
Let the edge of a surface area = a

Formula-
The surface area of a cube = 6a2
Where, a = edge of a cube.
Then, the surface area of a cube = 6a2

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 a2/8
Increased surface area = 75 a2/8 – 6 a2
= (75 a2 – 48 a2)/8
= 27 a2/8
Percentage of increased area = 27 a2 x 100/8 x 6 a2
= 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%.

Anurag Mishra Professor Answered on 7th August 2015.
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