Question

Diameter of cylinder A is $7$ cm, and the height is $14$ cm. Diameter of cylinder B is $14$ cm and height is $7$ cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Answer 1

Volume of cylinder B is greater than that of cylinder A.

We use the formulae:

$V=\pi r^{2}h$

$S=2\pi r(r+h)$

where,

V=volume of cylinder

S=surface are of cylinder

r= radius

h=height

Cylinder A:

$V=\pi r^{2}h\Rightarrow V=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 14=540$

$S=2\pi r(r+h)\Rightarrow S=2\times \frac{22}{7}\times \frac{7}{2}\times (\frac{7}{2}+14)=385$

Cylinder B:

$V=\pi r^{2}h\Rightarrow V=\frac{22}{7}\times {\left(\frac{14}{2}\right)}^2\times 7=1078$

$S=2\pi r(r+h)\Rightarrow S=2\times \frac{22}{7}\times \frac{14}{2}\times (\frac{14}{2}+7)=616$

It's clear from the calculation, that, cylinder with greater volume has greater surface area, i.e, cylinder B.