Question

ii) If each side of a cube is increased by 50% then the surface area of the cube

increases by​

Answer 1

Required Answer:-

Generally when it says surface area, it refers to Total surface area (TSA). And the formula for finding the TSA of the cube is:

Surface area of cube:

• TSA = 6(side)²

So,

Let initially the length of the side of the cube be s. Then the surface area of the cube will be:

➛ TSA = 6s²

Now the side is increased by 50%. That means,

➛ New side of the cube

= Side length + 50% of side length

= s + 1/2 of s

= 3/2 s

Then new surface area will be:

➛ New TSA = 6(3s/2)²

➛ New TSA = 6 × 9/4 s²

➛ New TSA = 9/4 × Previous TSA

The surface area now becomes 9/4 times of the initial surface area. Then percentage increase$:$

= New TSA - Old TSA / Old TSA × 100

= 9/4 s - s / s × 100

= 5/4s/s × 100

= 125%

Therefore:

• The surface area of the cube increases by 125%.

Answer 2

Answer:

the surface area of the cube increases by 125%

Step-by-step explanation:

Let the original side be a

surface area of cube = 6a^2

When each side of cube is increased by 50% side becomes 3/2 of original side (3/2a)

S = 6*(3/2a)^2 = 27a^2/2

Increase in surface area = 27a^2/2  - 6a2/6a2 *100% = 125%

125% is the answer