Each edge of a cube is increased by 50%.

What does the cube's surface area rise by in percentage terms?

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78%

50%

134%

125%

answer is D.

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Detailed Solution

Given- the edge of a cube is increased by 50%.
Let’s assume the edge of the given cube.
Edge of the cube = ‘a’.
Initial Surface area of cube= 6a² -eq.(1)
Find the new edge of the cube by increasing the existing edge by 50%.
The new edge of the cube =

a + 50100 a

-eq.(2

⇒ New edge of the cube= 100 a + 50 a 100

⇒ New edge of the cube 150 a 100

⇒ New edge of the cube 3 a 2

Now, we will find the surface area of the cube having an edge

3 a 2

.
Hence,
Final surface area (SA) of the cube =

6 × 3 a 2 2

⇒ S A = 6 × 3 a 2 × 3 a 2

⇒ S A = 27 a 2 2

-eq. (3)
After subtracting equation (1) from equation (3) we will get the increased surface area. i.e.
The increased surface area of cube =

27 a 2 2 − 6 a 2

-eq. (4)
Take the LCM of equation (4).
The increased surface area of cube =

27 a 2 − 12 a 2 2

The increased surface area of cube =

15 a 2 2

Now to find the percentage increase in the surface area of the cube.
The percentage increased in surface area of the cube =

Increased surface area Initial surface area × 100

⇒ % i n c r e a s e = 152 a 2 (6) a 2 × 100

⇒ % i n c r e a s e = 152 × 16 × 100 ⇒ % i n c r e a s e = 125 %

Thus, the percentage increased in surface area of the cube is 125% when each edge of a cube is increased by 50%.
Hence, option 4 is the correct option.

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