Question

if the length, breadth, height are doubled, them by hom much the total surface area will be increased​

Answer 1

Answer:

l'=2l

b'=2b &

h'=2h

total surface area of cuboid= 2(l'b'+b'h'+l'h')

=2(2l(2b)+2b(2h)+2l(2h))

=2(4(lb+bh+lh))

=4(2(lb+bh+lh))

=4(total surface area of cuboid before increasing dimensions)

therefore area increases by 4 units

Answer 2

Step-by-step explanation:

Given:-

the length, breadth, height are doubled

To find:-

if the length, breadth, height are doubled, them by hom much the total surface area will be increased ?

Solution:-

Let the length of a cuboid be l units

Let the breadth of the cuboid be b units

Let the height of the cuboid be h units

We know that

Total surface area of a cuboid

TSA = 2(lb+bh+hl) sq.units -----(1)

Now, If length is doubled then the length will be '2l' units

If Breadth is doubled then the breadth will be '2b' units

If Height is doubled then the height will be '2h' units

Then

Total Surface Area of the resulting cuboid =

2[(2l×2b)+(2b×2h)+(2h×2l)] sq.units

=> 2[4lb+4bh+4hl] sq.units

=>2×4(lb+bh+hl) sq .units

It can be written as

=> 4×2(lb+bh+hl) sq.units

=>4×TSA

=> 4×Total Surface Area of the original cuboid

(from (1))

=>4 Times to the total surface of the original cuboid

Answer:-

If the length, breadth, height are doubled, then the total surface area of the cuboid is increased to 4 times to the total surface area of the new cuboid .

Used formula:-

• Total surface area of a cuboid
• TSA = 2(lb+bh+hl) sq.units
• l=length
• b=breadth
• h=height