Question

How does the total surface area of a box changes if each dimension is doubled and 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... Let the Side of New cube whose dimensions are doubled be 2x

Total Surface Area of cube whose dimensions are doubled

= 6 × (2x)²

2... Let the Side of New cube whose dimensions are tripled be 3x

Total Surface Area of cube whose dimensions are tripled

= 6 × (3x)²

According to Question,

In each case,

Total Surface Area of New cube/Total Surface Area of original cube

1... 6 × (2x)²/6 × x²

= 4x²/x²

= 4

2... 6 × (3x)²/6 × x²

= 9x²/x²

= 9

1... If the dimensions of cube [box] be doubled then the total surface area of original cube will become 4 times the total surface area of new cube.

2... If the dimensions of cube [box] be tripled then the total surface area of original cube will become 9 times the total surface area of new cube.

#Be Brainly

Answer 2

$<b><i>(i) If each dimension is doubled then the total surface area becomes, = 2((4lb) + (4bh) + (4lh))</b>$

= 4 × [2(lb + bh + lh)]

∴ $<b><u>the area becomes four times.</u>$

(ii) If each dimension is tripled then the total surface area becomes, = 2((9lb) + (9bh) + (9lh))

= 9 × [2(lb + bh + lh)]

∴ the area becomes nine times.

$<u>$It is clear from the above two solutions that the area of cuboid becomes n^2 times the previous area if each dimension raised to n times.