How does the total surface area of a box change if each dimension is d

1.	How does the total surface area of a box change if each dimension is doubled ?
Answer» Let the original dimensions be Length – l units Breadth – b units Height – h units Then T.S.A = 2 (lb + bh + lh) If the dimensions are doubled then Length = 2l Breadth = 2b Height = 2h T.S.A. = 2 (2l. 2b + 2b . 2h + 2l . 2h) = 2 (4lb + 4bh + 4lh) = 4 × [2 (lb + bh + lh] = 4 × original T.S.A. i.e., T.S.A. increases by 4 times.

How does the total surface area of a box change if each dimension is doubled ?

Answer»

Let the original dimensions be Length – l units

Breadth – b units

Height – h units

Then T.S.A = 2 (lb + bh + lh)

If the dimensions are doubled then

Length = 2l

Breadth = 2b

Height = 2h

T.S.A. = 2 (2l. 2b + 2b . 2h + 2l . 2h)

= 2 (4lb + 4bh + 4lh)

= 4 × [2 (lb + bh + lh]

= 4 × original T.S.A.

i.e., T.S.A. increases by 4 times.