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 $369.6$ $cm^2$.