Theory:

A trash bin is in the shape of a cylinder of diameter \(28 \ cm\) and height \(40 \ cm\). Find the cost of painting the trash bin (including lid) at \(₹ 5\) per \(cm^2\). 
 
shutterstock_128273942 (1).jpg
 
Solution:
 
Diameter of the base \((d)\) \(=\) \(28 \ cm\)
 
Radius of the base \((r)\) \(=\) d2=282=14 \(cm\)
 
Height of the trash bin \((h)\) \(=\) \(40 \ cm\)
 
Total surface area of the cylinder \(=\) \(2 \pi r (r + h)\) sq. units
 
\(=\) \(2 \times \frac{22}{7} \times 14 (14 + 40)\)
 
\(=\) \(2 \times 22 \times 2 \times 54\)
 
\(=\) \(4752\)
 
Total surface area of the trash bin \(=\) \(4752\) \(cm^2\)
 
Cost of painting the trash bin per \(cm^2\) \(=\) \(₹5\)
 
Cost of painting the trash bin for \(4752\) \(cm^2\):
 
\(=\) \(4752 \times 5\)
 
\(=\) \(23760\)
 
Therefore, the cost of painting the trash bin is \(₹ 23760\).
 
Important!
The value of \(\pi\) should be taken as \(\frac{22}{7}\) unless its value shared in the problem.