Question

. If each edge of a cube is increased by 25%, then find the percentage increase in its surface area.
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Answer 1

GIVEN :-

• Each edge of cube is increased by 25%.

TO FIND :-

• % increase in its surface area.

TO KNOW :-

★ Area of cube = 6 × edge

SOLUTION :-

Let us consider , the initial edge of cube be 'x'.

We know , surface area of cube = 6×edge

Initial area = 6x

Now each edge of cube is increased by 25%.

→ New edge = x + 25% of x

→ New edge = x + (25/100) x

→ New edge = x + x/4

→ New edge = 5x/4

♦ New area = 6 × (5x/4)

♦ New area = 30x/4

♦ New area = 15x/2

______________________

% Increase in area

= [ (New area - initial area) / initial area ] × 100

= [ ( 15x/2 - 6x ) / 6x ] × 100

= [ ( 3x / 2 ) / 6x ] × 100

= [ 3x / 12x ] × 100

= [ 1/4 ] × 100

= 25

Hence , there is 25% increase in area when edge of cube is increased by 25%.

MORE TO KNOW :-

★ Area of Cylinder = πr²h

★ Area of Cone = (1/3) πr²h

★ Area of Cuboid = l × b × h

★ Area of Sphere = (4/3) πr³

★ Area of hemisphere = (2/3) πr³

Answer 2

$\bf{\blue{\;\;Given :}}$

• Each edge of a cube is increased by 25% .

$\bf{\green{\;\;To \: find :}}$

• Percentage increase its surface area

$\bf{\;\;\red{Solution :}}$

Let each side side of cube be 10 units

Then it's surface area = 6a² = 6 × 10² = 600 sq.units

New edge = 10 + 25% of 10 = 12.5 units .

Therefore ,

New Surface area = 6 × { 12 . 5 )² = 937.5 sq.units .

% increased =

$\frac{937.5 - 600}{600} \times 100 = 56.25\sf \: percent$

$\sf = 56.25 \: percent \: is \: the \: answer$