Question

if each side of cube is incresed by 50% find the percentage increse in its surface area

Answer 1

answer : 125%

Detailed SolutionGiven:

If each edge of a cube is increased by 50%

Formula used:

The surface area of cube = 6 side2

Calculation:

According to the question,

Let the side of the cube be x

Each side of the cube increased by 50%.

⇒ x(100 + 50)/100 = 1.5x

The surface area of the cube

⇒ 6 x2

The new surface area of the cube (side = 1.5x)

⇒ 6 × 2.25x2

Increase percentage in the surface area

⇒ ((6 × 2.25 x2 - 6 x2)/6 x2 }× 100

⇒ 125%

∴ The percentage increase in the surface area is 125%.

We know that

50% = 1/2

Let the edge of cube be 2 units

Increased edge = 3 units

Original surface area = 6 × 2 × 2 = 24 units2

Increased surface area = 6 × 3 × 3 = 54 units2

Percentage increase in area = (54 - 24)/24 × 100

∴ Percentage increase in area = 125%

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