# If Each Edge of a Cube is Increased by 50%, the Percentage Increase in Its Surface Area is - Mathematics

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MCQ

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

#### Options

• 50%

•  75%

• 100%

•  125%

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#### Solution

Let,

a →a Initial edge of the cube

A → Initial surface area of the cube

a' → Increased edge of the cube

A' → Increased surface area of the cube

We have to find the percentage increase in the surface area of the cube

Since it’s given that

a = a+axx50/100

= 3/2 a

We have,

A' = 6(a)^2

= 6 (3/2a)^2                { Since , a' = 3/2 a}

 = 9/4 (6a^2)

 =9/4 A

Percentage increase in surface area,

=(A'-A)/A xx 100

=(9/4 A-A)/A xx 100

=(5/4A)/A xx 100

= 125

Increase in surface area is 125% .

Concept: Surface Area of a Cuboid
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Exercise 18.4 | Q 21 | Page 36

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