5. Example problem of a right circular cylinder and hollow cylinder

1. 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 \(cm^2\). 

 

 

Solution:

 

Diameter of the base \((d)\) \(=\) \(28 \ cm\)

 

Radius of the base \((r)\) \(=\) $\frac{d}{2}=\frac{28}{2}=14$ \(cm\)

 

Height of the trash bin \((h)\) \(=\) \(40 \ cm\)

 

Total surface area of the right circular cylinder \(=\) \(2 \pi r (r + h)\) sq. units

 

\(=\) \(2 \times \frac{22}{7} \times 14 (14 + 40)\)

 

\(=\) \(2 \times 22 \times 2 \times 54\)

 

\(=\) \(4752\)

 

The 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 \(₹ 23760\).

 

 

2. The hollow cylinder height \(8.4 \ cm\) has the internal and external radii of \(2 \ cm\) and \(5 \ cm\), respectively. Find the curved surface area of the hollow cylinder.

 

Solution:

 

Height of the cylinder \(=\) \(8.4 \ cm\)

 

Internal radius, \(r\) \(=\) \(2 \ cm\)

 

External radius, \(R\) \(=\) \(5 \ cm\)

 

Curved surface area of a hollow cylinder \(=\) \(2 \pi (R + r)h\) sq. units

 

\(=\) \(2 \times \frac{22}{7} \times (5 + 2) \times 8.4\)

 

\(=\) \(2 \times \frac{22}{7} \times 7 \times 8.4\)

 

\(=\) \(2 \times 22 \times 8.4\)

 

\(=\) \(369.6\)

 

Therefore, the curved surface area of the hollow cylinder is \(369.6\) \(cm^2\).