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?

Volume of cylinder B is greater than A.

For cylinder A, 

Diameter = 7 cm, Radius = $\frac{7}{2}$cm and Height = 14 cm

 Volume of cylinder A $= \pi r^{2}h = (\frac{22}{7} )\times \left(\frac{7}{2}\right)\times \left(\frac{7}{2}\right)\times 14 = 539 c{m}^3$

For cylinder B, 

Diameter = 14 cm, Radius = 7 cm and Height = 7 cm

 Volume of cylinder B $= \pi r^{2}h = (\frac{22}{7} )\times \left(7\right)\times \left(7\right)\times 7 = 1078 c{m}^3$

Hence, Volume of cylinder B is greater than A.

Surface area of cylinder A$= 2\pi r(r+h ) = 2 x \frac{22}{7} x \frac{7}{2} x (\frac{7}{2} + 14) = 385 c{m}^2$

Surface area of cylinder B$= 2\pi r(r+h ) = 2 x \frac{22}{7} x 7 x (7 + 7) = 616 c{m}^2$

Yes,  the cylinder with greater volume also has greater surface area.