What will be the percentage increase in the area of the cube

Question

What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 20%?

A. 33%
B. 44%
C. 55%
D. 56%
E. 73%

JubtaGubar · Answer

The question is very easy. My logic is the following:
A surface = 6*a^2
After 20% increase A surface = 6* ((1.2a)^2) = 6*1.44*a^2
The increase in the surface area = (6*1.44*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.44-1))/(6*a^2) = 1.44-1=0.44 = 44%

but the official answer is different...

Could you please advise what is wrong with my solution or the official answer is not correct?

Bunuel · Answer

Your solution is correct.

Say the edge of the cube is 10, its surface area is 6*100;
After 20% increase the edge becomes 12, so the new surface area is 6*144;

Percent increase=change/original=(6*144-6*100)/(6*100)*100=44%.

Or directly: the new surface area is 6*144=(6*100)*1.44 --> increase 44%.

Answer: B.

fthtnrvr · Answer

If you increase a line with %20 it the line will be 1,2/1 
If we increase edges with %20 in a surface the area will be 1.2*1.2 =1.44
If we increase edges with %20 in a cube or 3D , the volume is 1.2*1.2 = 1.2*1.2*1.2

Your solution is correct but in order to minimize time to solve

It doesn't matter how many surface have a 3D object or how many edges have a 2D object
So you dont have to think about how many surface does it have.

The ratio of line increase with (100+A)^1
The ratio of area will be (100+A)^2
The ratio of volume will be (100+A)^3

In line the increase or decrease will be also linear. (100+A/100)
In 2D it will be (100+A/100)*(100+A/100) \ second power
In 3D it will be (100+A/100)*(100+A/100)*(100+A/100) \third power

All you need to do is just multiply 1.2 * 1.2 = 1.44 and so it is %44 
That's all

harshavmrg · Answer

just like others, even i got 44% increase...but dont know OA says answer is D.....

JubtaGubar · Answer

Now I am sure that it is a mistake in the OA. I changed it to B.

Thank you all for confirming my solution!

SchruteDwight · Answer

6(10)^2 –> 6(12)^2

(864-600)/600*100=264/6

Kinshook · Answer

Asked: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 20%?

Surface area of a cube = 6a^2
New a = 1.2a
New surface area of the cube = 6 (1.2a)^2 = 1.44 * 6a^2 = 44% increase

IMO B

Archit3110 · Answer

Cube SA ; 6s^2 
s=1 ; CSA ; 6
s=1*1.2 ; CSA ; 6*(1.2)^2
%∆ ; 6*(1.2)^2-6/6 ; ( 1.44-1) ; 44%
IMO B

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What will be the percentage increase in the area of the cube

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What will be the percentage increase in the area of the cube

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