Question

hieght, breadth and length of a box are in the ratio 1:2:4, of height, breadth and length of another box are 25% less, 50% less and 25% greater respectively, then the surface area of the first box is less/more than that of the second box by?​

Answer 1

First box has the bigger SA

Answer 2

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• Surface Area of cuboid = 2(L * B + B * H + H * L)

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Height , Breadth & Length of First Box are 10x, 20x & 40x Respectively.

Than,

→ Surface Area of First Box = 2(40x*20x + 20x*10x + 10x*40x) = 2(800x² + 200x² + 400x²) = 2*1400x² = 2800x².

Now,

→ Height of Another Box = 10x - (25% of 10x) = 10x - 2.5x = 7.5x .

→ Breadth of Another Box = 20x - (50% of 20x) = 20x - 10x = 10x .

→ Length of Another Box = 40x + (25% of 40x) = 40x + 2.5x = 50x .

So,

→ Surface Area of Another Box = 2(50x*10x + 10x*7.5x + 50x*7.5x) = 2(500x + 75x + 375x) = 2*950 = 1900x².

Therefore,

→ Surface Area of First Box - Surface Area of Another Box = 2800x² - 1900x² = 900x².

→ Required % More = (900x² * 100) / (2800x²) = 32.14% (Ans).

Hence, we can conclude That, the surface area of the first box is 32.14% more than that of the second box ..

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⟪Note :- Since Sides Ratio is Given We can't Find Exact value of More Surface Area . But we can Find Exact value of Percentage More . ⟫

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