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The edge of a cube is increased by 20%. What is the percentage increase in its surface area?

 

 Jun 14, 2020
 #1
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SA of a cube =6a^3, a=edge.

If a = 1, the SA =6

If a =1.2, the SA =6*1.2^3 =10.368

10.368 / 6 =1.728 - 1 x 100 =72.8% increase in SA of the cube.

 Jun 14, 2020
 #3
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The total surface area of the cube should be 6a2, not 6a3. (Explanation in my answer.)

MaxWong  Jun 14, 2020
 #2
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A cube has 6 faces of equal sizes. Each side has area a2, where a is the length of an edge.

 

Therefore the total surface area of the cube is 6a2.

 

After increasing the edge length by 20%, the edge is now of length 1.2a.

 

The new total surface area is 6(1.2a)2, which is (1.2)2 = 1.44 times greater than the original.

 

Therefore the total surface area is increased by (1.44 - 1) = 44%

 Jun 14, 2020

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