If all the sides of a cuboid are increased by 20 then by what percentage does its volume increase

Hello Prasad !

Formula for Volume of cuboid is , (length × breadth × height) cubic units.

So , if length is  increased by 20% which means new length is 1.2 time of old length , similarly , new breadth will become 1.1 time more and height will become 0.95 times of old height , as it decreased.

So now , new volume will become , 1.2 * length × 1.1*breadth × 0.95*height ,

1.254 * length × breadth × height ,

Which means it get increased by 25.4 %

Hope it helps !

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If all the sides of a cuboid are increased by 20 then by what percentage does its volume increase

Given:

Increase in length of cuboid = 20%

Increase in breadth of cuboid = 30%

Increase in height of cuboid = No change

Formula Used:

Volume of a Cuboid = l × b × h

where,

l = Length of the cuboid 

b = Breadth of the cuboid

h = Height of the cuboid

Calculation:

According to the question,

Initial volume of the cuboid = l × b × h = lbh

Again, According to the question,

New length of cuboid = (120/100) × l

⇒ (6/5) × l

& New breadth of cuboid = (130/100) × b

⇒ (13/10) × b

So, New volume of cuboid = (6/5) × l × (13/10) × b × h

⇒ (6/5) × (13/10) × lbh

⇒ (78/50) × lbh 

⇒ (156/100) × Intial volume of the cuboid

Now, Required percentage = {(New volume - Initial volume)/Initial volume} × 100%

⇒ [{(156/100) × lbh - lbh}/lbh] × 100%

⇒ {(156 - 100)/100} × 100%

⇒ (56/100) × 100%

⇒ 56%

∴ The new volume of the cuboid is 56% greater than the initial volume of the cuboid.

We can use successive percentage method to solve this

When there is increase of a% and b% then the overall percentage change is a + b + ab/100

As Volume of cuboid depends on length, breadth and height but there is no change in height then the change in volume will only depend on two factors (i.e. length and breadth)

Percentage change in volume = 20 + 30 + (20 × 30)/100 = 50 + 6 = 56%

∴ The new volume of the cuboid is 56% greater than the initial volume of the cuboid.

If length, breadth and height of a cuboid are increased by 20 %, what is the percentage increase in the the total surface area of cuboid? [3 MARKS]

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