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Q.

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

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a

50

b

125

c

150

d

300

answer is B.

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Detailed Solution

Question Image

S = 6a2
Since, the edge length of the cube is increased by 50%, therefore
a1 =

(a + \frac{50}{100} \times a)

⇒ a1 = (a + 0.5a)
⇒ a1 = 1.5a
Substitute, 1.5a for a in the above surface area formula to obtain the new surface area S1 of the cube.
S1 = 6(1.5a)2
⇒ S1 = 6(2.25a2)
The percentage increase in the surface area of the cube is calculated as shown below.
The percentage increase in the surface area =

\frac{S_{1} - S}{S}

× 100
Substitute, 6a2 for S, 6(2.25a2) for S1 in above formula.
The percentage increase in the surface area =

\frac{6 (2.25 a^{2}) - 6 a^{2}}{{6 a}^{2}}

× 100
The percentage increase in the surface area =

\frac{6 a^{2} (2.25 - 1)}{{6 a}^{2}}

× 100
The percentage increase in the surface area = 1.25 × 100
The percentage increase in the surface area = 125
Hence, option 2 is correct.

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