Question

if the lengh of each edge of a cube inceases by 50%, what is the percentage increase in the total surface of the cube
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Answer 1

First, Let us calculate the total surface area of a cube of edge ( side ) a units before increasing its edge by 50%.

We know,

⇒ Total Surface Area of Cube = 6(Side)²

⇒ TSA₁ = 6a² ...(1)

Now, Increasing the edge of the cube by 50%, we get

⇒ new Edge = 50% of a + a

⇒ new Edge = a + 50a/100

⇒ new Edge = 3a / 2

So,

⇒ TSA₂ = 6 × (3a/2)²

⇒ TSA₂ = 6 × 9a² / 4

⇒ TSA₂ = 27a² / 2 ...(2)

Now, To Find the percentage increase in the total surface area, We first need to find the ratio of the surface areas and multiply it by 100 to get the percentage.

⇒ ( TSA₂ / TSA₁ ) × 100

⇒ (27a² / 2 ) / (6a² ) × 100

⇒ 27a² / 12a² × 100

⇒ 27/12 × 100

⇒ 2.25 × 100

⇒ 225%

Hence, The total surface area will increase by 225%