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State true or false.

If each edge of a cube is increased by 50 %, the percentage increase in the surface area is 50%.

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True

False

answer is B.

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Detailed Solution

We have to check if the percentage increase in the surface area is 50%.
We know that,
The surface area of the cube

= 6 (s i d e) 2

.
Note that, each edge of a cube is increased by

50 %

.
Suppose the original edge of the cube is

a u n i t s

, so, the original surface area of the cube

= 6 a 2 u n i t s

.
Hence, new edge of the cube:
= 150
Thus, new surface area:

= 6 × 3 a 2 2 = 27 a 2 2

Calculating the increase in area.

= 27 a 2 2 − 6 a 2 = 15 a 2 2

Calculating

%

increase in surface area.

= 15 a 2 2 × 1 6 a 2 × 100 % = 125 %

So, the percentage increase in the surface area is

125 %

and thus the statement is false.
Therefore, option 2 is correct.

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