Question

How does the total surface area of a box change if 1)each dimension is doubled?
2)each dimension is tripled?

Answer 1

Solution -

​​Let the side of original cube be x  

Total Surface Area of original cube  

= 6 × x²    [ ∵ TSA of cube = 6 × Side² ]  

1. So, the side of new cube[I] be 2x  

Total Surface Area of new cube1    

= 6 × (2x)²    

2. So, the side of new cube[II] be 3x

Total Surface Area of new cube2  

= 6 × (3x)²  

 According to Question,

1... TSA of new cube[I] / TSA of ori. cube   

= 6 × (2x)² / 6 × x²  

= 4x² / x²  

= 4  

∴ Total Surface Area of new cube[I]       = 4 times Total Surface Area of original cube    

2... TSA of new cube[II] /TSA of ori. cube    

= 6 × (3x)² / 6 × x²  

= 9x² / x²  

= 9    

∴ Total Surface Area of new cube[II]      = 9 times Total Surface Area of original cube  

#Be Brainly

Answer 2

Here is your perfect answer

thank you