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Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

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#### Solution

`"Let d be the edge of the cube"`

`∴surface area of cube= 6xxa^2`

i.e, `S_1=6a^2`

According to problem when edge increased by 50% then the new edge becomes

`=a+50/100xxa`

`=3/2a`

`"New surface area becomes" =6xx(3/2a)^2`

i.e.,`=6xx9/4a^2`

`s_2=27/2a^2`

∴Increased surface Area = `27/2a^2-6a^2`

`=15/2a^2`

So, increase in surface area `(15/2a^2)/6a^2`

`=15/12xx100`

`=125%`

Concept: Surface Area of a Cuboid

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