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How does the total surface area of a box change if
Each dimension is doubled?
Express in words. Can you find the area if each dimension is multiplied n times?

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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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