# If the side of a cube is increased by 50%, then what percent increase will be in the area of the vertical faces of the cube?

A. 125%

B. 150%

C. 100%

D. 50%

Answer

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Hint: We have to find out the percent increase in the area of the faces of the cube, so we will make use of the formula of the area of the cube and try to solve this.

Complete step-by-step answer:

Let us consider the side of the cube =a

Given that the side of a cube is increased by 50%

So, the side a is increased by 50%

So, the increase would be=$\dfrac{{50}}{{100}}a = \dfrac{1}{2}a = 0.5a$

So, from this we can write, the new side=length of the original side+ increase in length

The new side = 1+0.5a=1.5a

Now, the area of the 4 walls(old)=$4{a^2}$

Area of the 4 walls(new)=$4 \times {(1.5a)^2} = 4 \times 2.25{a^2} = 9{a^2}$

Increase in the area of the wall=$9{a^2} - 4{a^2} = 5{a^2}$

Now, the % increase in the area of the wall=$\dfrac{{increase{\text{ in the area}}}}{{original{\text{ area}}}} \times 100 = \dfrac{{5{a^2}}}{{4{a^2}}} \times 100 = \dfrac{5}{4} \times 100 = 5 \times 25$ =125

So, from this we can say that the % increase in the area=125%

So, option A is the correct answer.

Note: When solving these type of questions, make sure to first find out the new area after the side of the cube has been increased and then calculate the percentage increase with respect to the original area of the side.

Complete step-by-step answer:

Let us consider the side of the cube =a

Given that the side of a cube is increased by 50%

So, the side a is increased by 50%

So, the increase would be=$\dfrac{{50}}{{100}}a = \dfrac{1}{2}a = 0.5a$

So, from this we can write, the new side=length of the original side+ increase in length

The new side = 1+0.5a=1.5a

Now, the area of the 4 walls(old)=$4{a^2}$

Area of the 4 walls(new)=$4 \times {(1.5a)^2} = 4 \times 2.25{a^2} = 9{a^2}$

Increase in the area of the wall=$9{a^2} - 4{a^2} = 5{a^2}$

Now, the % increase in the area of the wall=$\dfrac{{increase{\text{ in the area}}}}{{original{\text{ area}}}} \times 100 = \dfrac{{5{a^2}}}{{4{a^2}}} \times 100 = \dfrac{5}{4} \times 100 = 5 \times 25$ =125

So, from this we can say that the % increase in the area=125%

So, option A is the correct answer.

Note: When solving these type of questions, make sure to first find out the new area after the side of the cube has been increased and then calculate the percentage increase with respect to the original area of the side.

Last updated date: 17th Sep 2023

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