Question

Express in words. Can you find the total surface area of the box if each dimension is raised
to n times?






​

Answer 1

Step-by-step explanation:

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.