How does the total surface area of a box changed if each dimension is doubled?
A) T.S.A. of the box will become 4 times of original area.
B) T.S.A. of the box will become 3 times of original area.
C) T.S.A. of the box will become 6 times of original area.
D) T.S.A. of the box will become 8 times of original area.
Correct option is (A) T.S.A. of the box will become 4 times of original area.
Let \(l,b\;and\;h\) are parameters of original box.
\(\therefore\) \(2l,2b\;and\;2h\) are parameters of new box.
\(\therefore\) Total surface area of new box \(=2\,(2l\times2b+2b\times2h+2h\times2l)\)
\(=8\,(lb+bh+hl)\)
\(=4\times2\,(lb+bh+hl)\)
\(=4\times\) Total surface area of original box
Thus, if each dimension is doubled of a box then total surface area of box will become 4 times of original area.