Aptitude - Volume and Surface Area - Discussion

1 cubic centimeter equal to 1 millilitre volume of liquid, in this question silver metal liquid is used to make a wire, the wire is in the shape of cylinder , so we have to form silver wire, then 66 cubic centimeter silver metal liquid is changed to volume of the wire (Wire is in the form of cylinder, assume long thin wire. The length of the wire is also the height of the cylinder) then by using formula of the volume of the cylinder we can find the length of the wire, the formula is:
V = πr^2h.
Radius = diameter/2 = 1/2 mm
i.e To convert mm to cm use the following formula:
1 mm = 0.1 cm.
So, to convert 0.5 mm to cm, multiply 0.1 by 0.5.
i.e. 0.5 mm = 0.1 * 0.5 cm = 0.05 cm or 1/20 cm.
Then according to formula,
66 cubic cm silver metal liquid is equal to the volume of the wire.
Then, 22/7 * 1/20 * 1/20 * h = 66.

h = 66 * 20 * 20 * 7/22,
= 8400 cm,
= 84 m.

Actaully wire is of the form:: CYCLINDER

we know,
volume of cyclinder = π*r^2* h----------- (1)

r-radius
h-height(lenth)
Given
Diameter(d)=1mm
so r=d/2
r=(1/2)mm
r=(1/20)cm

Substitute in Eqn (1)

22/7 * (1/20)^2 *h =66 (given)

h =66 x 20 x 20 x 7/22
= 8400 cm = 84 m.

They have given d diameter. But we need radius. So when 1 mm is divided by 2, we get 1/2 mm and to convert mm into cm we have to multiply it by 10.

Therefore, 1/2 multiply by 10, we get 1/20.

v.ocyclinder= πr^2h.

Where π equals to 22/7.
22/7*1/20*1/20*h = 66,
11h/1400 = 66,
h = 92400/11,
h = 8400cm,
h = 8400/100m,
h = 84m.

1/2 * 10 = 5 >_<.

But.

1/2 = .5 mm.

And to convert it into cm we have to divide it by 10.

So, .5/10 = .05cm.

5/100 = 1/20 cm.

@Ayush.

Because the wire is so small people don't tend to think of it as a cylinder but it is.

It is long and has very small radius!

1/2 mm is (1/2)*10^-3 or (1/2)* 1/1000 or (1/20)* (1/100) or (1/20)*10^-2 .

10^-2 metre is nothing but centimetre

We know that d = 2r then r = d/2mm and here d is given 1mm and 1mm convert in cm then r = 1/20cm.

@Rashmi, @Megha.

1cm=10mm.
? =1/2mm.
Cross multiplication

1/2 * 1/10.
= 1/2 * 10.
= 1/20 m.

Simple. The volume is given in mm and the length in meters. Hence the length should be minimal.