Question

Twenty cylindrical pillars of the parliament house are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4m. What will be the cost of cleaning them at the rate of Rs. 250 per square metre?

Answer 1

Hint: The cleaning is done on the surface of pillars, hence we are required to find the curved surface area (CSA) of the sphere as pillars are cylindrical in shape.
\[{\text{CSA of cylinder }} = 2\pi rh\]

Complete step-by-step answer:

The diameter of cylinder = 0.50 m (Given)
Therefore, radius $ = \dfrac{{0.50}}{2}m{\text{ }}\left( {{\text{As radius}} = \dfrac{{{\text{Diameter}}}}{2}} \right)$.
Radius(r) = 0.25 m
Height = 4 m (Given)
We know,
\[{\text{CSA of cylinder }} = 2\pi rh\]
Substituting the values, we get:
\[2\pi rh = 2 \times \dfrac{{22}}{7} \times 0.25 \times 4\]
As;
$
  \pi = \dfrac{{22}}{7} \\
  r = 0.25 \\
  h = 4 \\
$
\[ = 2 \times \dfrac{{22}}{7} \times \dfrac{{25}}{{100}} \times 4\] (To remove decimal)
$ = 2 \times \dfrac{{22}}{7}$
\[ = \dfrac{{44}}{7}{m^2}\]
CSA of 20 pillars \[ = \dfrac{{20 \times 44}}{7}{m^2}\]
Calculating cost of cleaning:
It is given that cost of cleaning per m2 is Rs. 2.50, therefore cost of cleaning 20 pillars is given by:
CSA of 20 pillars x cost of cleaning per m2 \[ = \dfrac{{20 \times 44}}{7} \times 2.5{\text{ Rs}}{\text{.}}\]
= Rs. 314.28
Therefore the cost of cleaning 20 pillars of diameter 0.5 cm and height 4 m at Rs. 2.50/ m2 is Rs. 314.28.

Note: In cases like cleaning, painting, decorating etc. the curved surface area is always found.The value can be converted to decimals but further multiplication becomes easier with fractions.