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

The heights and diameters of these cylinders A and B are interchanged. 
We know that, 
Volume of cylinder = \(\pi r^2h\)
If measures of r and h are same, then the cylinder with greater radius will have greater area.
Radius of cylinder A = \(\frac{7}{2}\) cm 

Radius of cylinder B = \(\frac{14}{2}\) cm = 7 cm 
As the radius of cylinder B is greater, therefore, the volume of cylinder B will be greater.
Let us verify it by calculating the volume of both the cylinders. 
Volume of cylinder A = \(\pi r^2h\)
\(= (\frac{22}{7} )×(\frac{7}{2})×(\frac{7}{2})×14 = 539\) cm³
Volume of cylinder B = \(\pi r^2h\)
\(= (\frac{22}{7})×7×7×7 = 1078 \) cm³

Volume of cylinder B is greater. 
Surface area of cylinder A = \( 2\pi r(r+h )\)
\(= 2 \times \frac{22}{7} \times \frac{7}{2} \times (\frac{7}{2} + 14) = 385\)
Surface area of cylinder A is 385 cm²

Surface area of cylinder B \(=2\pi r(r+h )\)
\(= 2×(\frac{22}{7})×7(7+7) = 616\)
Surface area of cylinder B is 616 cm²
Thus, the surface area of cylinder B is also greater than the surface area of cylinder A.