Question

How does the total surface area of a box change if
(I) Each dimension is doubled?
(ii) Each dimension is tripled?​

Answer 1

The formula for a surface area of a cuboid (TSA) is =2(lb+bh+hl)

Where l = length , b = breadth , h=height .

Accrding to the question if Each dimesion is doubled then

⇒TSA

′

=2[(2l×2b)+(2h×2b)+(2l×2h)]

⇒TSA

′

=4×2(lb+bh+hl)

⇒TSA

′

=4×TSA

Hence the new TSA is 4 times the original TSA .

Now if each dimension is multiplied n times :

⇒TSA

′

=2(nl×nb)+(nb×nh)+(nl×nh)

⇒TSA

′

=n

2

×2(lb+bh+hl)

⇒TSA

′

=n

2

×TSA

Thus if the dimesions are multiplied n times the area will become n

2

times the original area.

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