Question

If 'V' is the volume of a cuboid of dimensions a xbxc and 'S' is its surface area, then prove
that:
​

Answer 1

Answer:

ANSWER

The dimensions of the cuboid are a,b,c.

We know that, Volume of the cuboid V=abc and surface area of the cuboid S=2(ab+bc+ac)

To prove:

V

1

=

S

2

[

a

1

+

b

1

+

c

1

]

Consider LHS,

V

1

=

abc

1

...(1)

Consider RHS.

S

2

[

a

1

+

b

1

+

c

1

]=

2(ab+bc+ac)

2

[

a

1

+

b

1

+

c

1

]

=

ab+bc+ac

1

[

a

1

+

b

1

+

c

1

]

=

ab+bc+ac

1

[

abc

ab+bc+ac

]

=

abc

1

S

2

[

a

1

+

b

1

+

c

1

]=

abc

1

...(2)

Hence from (1) and (2) we get

V

1

=

S

2

[

a

1

+

b

1

+

c

1

]