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If the length, breadth and height of a cube are decreased, decreased and increased by 5%, 5% and 20%, respectively, then what will be the impact on the surface area of the cube (in percentage terms)?
  • a)
    6.0833%
  • b)
    5%
  • c)
    8.33%
  • d)
    7.25%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the length, breadth and height of a cube are decreased, decreased ...
Assume the initial surface area as 100 on each side. A total of 6 such surfaces would give a total surface area of 600. Two surface areas would be impacted by the combined effect of length and breadth, two would be affected by length and height and two would be affected by breadth and height. Thus, the respective surface areas would be (90.25 twice, 114 twice and 114 twice) Thus, new surface area = 180.5 + 456 = 636.5.
A percentage increase of 6.0833%.

Hence Option A is correct

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Most Upvoted Answer
If the length, breadth and height of a cube are decreased, decreased ...
Given,
Length, breadth and height of a cube are decreased by 5%, 5% and increased by 20% respectively.

Let the original length, breadth and height of the cube be L, B and H respectively.

After the given changes, the new dimensions of the cube will be:
Length = 0.95L
Breadth = 0.95B
Height = 1.20H

The surface area of a cube is given by 6L^2

The new surface area of the cube will be:
6(0.95L)^2 = 6(0.9025L^2)
= 5.415L^2

The percentage change in surface area can be calculated as:
= ((New surface area - Original surface area)/Original surface area) * 100
= ((5.415L^2 - 6L^2)/6L^2) * 100
= -9.1667%

Therefore, the percentage decrease in surface area of the cube is 9.1667%.

However, we are asked for the percentage impact on surface area, which is the absolute value of the percentage change in surface area. Hence, the answer is:
= |9.1667%|
= 6.0833%

Therefore, the percentage impact on surface area of the cube is 6.0833% (Option A).
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Each question is followed by two statements, A and B. Answer each question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q. If the breadth of a rectangle is increased by 2 units and the length is decreased by 3 units, the area is unchanged. What is the area of the rectangle?A. If the breadth is decreased by 1 unit and the length is increased by 3 units, the area remains the same.B. If the breadth is increased by 1 unit and the length is increased by 2 units, the area gets doubled.

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If the length, breadth and height of a cube are decreased, decreased and increased by 5%, 5% and 20%, respectively, then what will be the impact on the surface area of the cube (in percentage terms)? a) 6.0833%b) 5%c) 8.33%d) 7.25%Correct answer is option 'A'. Can you explain this answer?
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