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How does the total surface area of a box change if
Each dimension is tripled?
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 tripled then ⇒TSA ′ =2[(3l×3b)+(3h×3b)+(3l×3h)] ⇒TSA ′ =9×2(lb+bh+hl) ⇒TSA ′ =9×TSA Hence the new TSA is 9 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 dimensions are multiplied n times the area will become n 2 times the original area.
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