if v is the volume of cuboid of dimensions a, b, c and s is it's surface area, then prove that
¹/v = ²/s(¹/a + ¹/b + ¹/c)
Answers
Step-by-step explanation:
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
]
Step-by-step explanation:
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 = S2 [ a1 + b1 + c1 ]
Consider LHS,
V1 = abc1
...(1)
Consider RHS.
S2 [ a1 + b1 + c1 ]= 2(ab+bc+ac)2 [ a1 + b1 + c1 ] = ab+bc+ac1 [ a1 + b1 + c1 ]
= ab+bc+ac1 [ abcab+bc+ac ]
= abc1
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
]