Question

The ratio of linear to volume expansion of a cube is 1:12. Find side of the cube.
(A) 2 cm
(B) 6 cm
(C) 5 cm
(D) 3 cm​

Answer 1

Given : The ratio of linear to volume expansion of a cube is 1 : 12.

To find : side length of cube.

solution : linear expansion of side length of cube is given by, $\Delta a=a_0\alpha\Delta T$

and volume expansion of volume of the cube is given by, $\Delta v=v_0\gamma\Delta T$

we know, $\gamma=3\alpha$

volume of cube = (side length)³

so, $v=a_0^33\alpha\Delta T$

as it is given that the ratio of linear to volume expansion is 1 : 12.

⇒∆a/∆v = $a_0\alpha\Delta T$/$a_0^33\alpha\Delta T$

⇒1/12 = 1/$3a_0^2$

⇒$a_0^2$ = 4

⇒$a_0$ = 2

Therefore the side length of the cube is 2 cm.

Therefore option (A) is correct choice.

Answer 2

Given : The ratio of linear to volume expansion of a cube is 1:12

To find : side of the cube.

Solution:

Let say Side of Cube  =  a  cm

Volume = Side³  = a³  cm³

V  = a³

dV/dt   = 3a²da/dt

=>(da/dt)/(dV/dt )  = 1/3a²

(da/dt)/(dV/dt )  = 1/12

Comparing both

1/3a² = 1/12

=> a² = 4

=> a = 2

side of the cube = 2 cm

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25 Oct 2019 ... amitnrw. don