Question

Chapter : Surface Area and Volume [ Class : IX ]

Question: Each side of a cube is increased by 50%. Then the surface area of the cube is increased by:
i)50%
ii)100%
iii%125%
iv)150%

Hint: The answer is option (iii)

I am unable to find how, please help...

PLEASE ANSWER AS SOON AS POSSIBLE !!!

Answer 1

Answer:

increase % in total surface area of cube=125%

increase % in lateral surface area of cube=125%

Step-by-step explanation:

Answer 2

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%