Question

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

Options

• 50%

•  75%

• 100%

•  125%

Answer 1

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% .