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

1.	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.
Answer» 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. A) T.S.A. of the box will become 4 times of original area.

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.

Answer»

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.

A) T.S.A. of the box will become 4 times of original area.