Aptitude - Volume and Surface Area - Discussion

Because, the VOLUME OF HOLLOW CYLINDER FORMULA is π(R^2-r^2)h.
Assume, (hollow iron pipe is in the shape of a hollow cylinder).
Here, we require RADIUS, but in question, it is in DIAMETER.
Outer dia=8cm[R=d/2=4cm];;then thickness=1cm(I.e, reduce diameter Of outer pipe by 2cm)..since thickness is both sides of pipe..(thickness = 1+1)
This gives diameter Of inner pipe = 6cm[r=d/2=3cm].
Then substitute R&r in formula....
Volume = 22/7 * (4^2 - 3^2) * 21 = 22 * (16 - 9) * 3 = 22*(7)*3 = 462 cm3.
Weight = density * volume.
= 8 * 462 = 3696 g.
= 3696/1000 = 3.696 kg.

Because, the VOLUME OF HOLLOW CYLINDER FORMULA is π(R^2-r^2)h.
Assume, (hollow iron pipe is in the shape of a hollow cylinder).
Here, we require RADIUS, but in question, it is in DIAMETER.
Outer dia=8cm[R=d/2=4cm];;then thickness=1cm(I.e, reduce diameter Of outer pipe by 1cm).

This gives diameter Of inner pipe = 7cm[r=d/2=3.5cm].
Then substitute R&r in formula,
Volume = 22/7 * (4^2 - 3.5^2) * 21 = 22 * (16 - 12.25) * 3 = 22*(3.75)*3 = 247.5 cm3.
Weight = density * volume.
= 8 * 247.5 = 1980 g.
= 1980/1000 = 1.98 kg.

Convert hollow cylinder into the metal sheet.


Hollow cylinder

h=21cm
Thickness=1cm

Metal sheet
b=21cm
h=1cm

loop length of the cylinder will become the length of the metal sheet.
The loop length=2*π*r, r=4cm.

The volume of metal sheet
= lbh = (2*π*4)*21*1=527.52 cu.cm.
weight=8*527.52=4220.16 gm=4.220 kg

is this wrong? if this so, explain me.

The external Diameter is given 8 cm and the thickness of the pipe is given 1 cm.
Hence, the External radius (R) would be 4 cm & Internal radius(r) would be (8 - 1 - 1)/2 = 3cm.

And the volume will be PI*(R*R - r*r)*h = (22/7)*(4*4 - 3*3)*21 = (22/7)*(16-9)*21 = 462 g.
Therefore, weight of the pipe = (462*8) g = 3696 g = 3.696 kg.

External diameter = 8 cm.
External radius = R =4 cm.
Given Thickness= 1 cm.

So, internal diameter= (8-1) cm = 7 cm.
Internal radius = r = 3.5 cm not 3 cms.

According to the volume of iron;

= 21*(22/7)*(16-12.25),
= 247.5 cm3.

Weight of iron = 247.5* 8 = 1980 gram or 1.98 kg.

External diameter = 8 cm.
External radius = R =4 cm.
Given Thickness= 1 cm.

So, internal diameter= (8-1) cm = 7 cm.
Internal radius = r = 3.5 cm not 3 cms.
According to the volume of iron;

= 21*(22/7)*(16-12.25),
= 247.5 cm3.

Weight of iron = 247.5 * 8 = 1980 gram or 1.98 kg.

The Internal radius and external radius. given is 8g/cm^3 not for hollow space.So, the first find out the full volume that is with the use of external radius. Now subtract hollow space that volume with internal radius. R^2h*r^2h.

Volume = base area * height.

For calculating, base area of the given hollow cylinder, we should remove the area containing thickness from the original.

So (pi * 4^2) - (pi*3^2) = pi* (4^2 - 3^2) = Effective base area.

@Sai Dileep. The formula for volume to be applied here is the cylinder.

@Rajadurai. Since the pipe is hollow so the internal part is being subtracted from the total thickness, which is the radius.

@Divya as per formula, it means cylinder volume is,

pi*r^2h, here it is a hollow cylinder we have to subtract external diameter to internal diameter.