Q. 434.2( 18 Votes )

# If each edge of a

Answer :

Given: Edge of a cube is increased by 50%

Let ‘a’ be the Edge of the cube

Area of the cube is : 6l^{2} (where ‘l’ is the edge of a cube)

Let A_{1} be the initial surface area of the cube.

∴ A_{1} = 6a^{2}

Now,

50% of the edge is: a × =

∴ Edge = a + after increasing edge by 50%

That is edge of the cube after increasing it by 50% is

Let A_{2} be the surface area of the cube after increasing the edge by 50%

∴ A_{2}= 6 × ()^{2} = × 6a^{2}

Here increase in area = A_{2} –A_{1}

⇒ increase in area = × 6a^{2} – 6a^{2} = × 6a^{2}

Now, increase in percentage is:

Increase in % = × 100 = × 100 = 125%

∴ If each edge of a cube is increased by 50%, then the percentage increase in the surface area is 125%

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