Question

There is a cylindrical platform of 2 m radius, 50 cm height in the school playground. What will be the cost of white washing the curved surface of this platform at the rate of Rs 12.5 per 100 sq. cm ($\pi = 3.14$)

Answer 1

Hint: Here, we will proceed by using the formula CSA$ = 2\pi rh$ in order to calculate the curved surface area of the given cylindrical platform which is getting white washed. Then, we will multiply the rate of white washing with the curved surface area to get the total cost of white washing.

Complete step-by-step answer:

As, 1 meter = 100 centimeter i.e., 1 m = 100 cm
Given, radius of the cylindrical platform is r = 2 m = 200 cm
Height of the cylindrical platform is h = 50 cm
As we know that the curved surface of any cylinder having radius r and height h is given by
CSA$ = 2\pi rh{\text{ }} \to {\text{(1)}}$
Using the formula given by equation (1), we get
Curved surface area of the cylindrical platform$ = 2\pi rh$
By putting r = 200 cm, h = 50 cm and $\pi = 3.14$ in the above equation, we get
$ \Rightarrow $Curved surface area of the cylindrical platform$ = 2 \times 3.14 \times 200 \times 50 = 62800{\text{ c}}{{\text{m}}^2}$
It is also given that the rate of white washing the curved surface of the cylindrical platform = Rs 12.5 per 100 ${\text{c}}{{\text{m}}^2}$
$ \Rightarrow $Rate of white washing the curved surface of the cylindrical platform = Rs $\dfrac{{{\text{12}}{\text{.5}}}}{{100}}$ per ${\text{c}}{{\text{m}}^2}$
Total cost of white washing the curved surface of the cylindrical platform = (Rate of white washing the curved surface of the cylindrical platform)$ \times $(Curved surface area of the cylindrical platform)
$ \Rightarrow $ Total cost of white washing the curved surface of the cylindrical platform$ = \left( {\dfrac{{{\text{12}}{\text{.5}}}}{{100}}} \right) \times 62800 = {\text{Rs }}7850$.

Note: In this particular problem, the given value of rate of white washing which is Rs 12.5 per 100 sq. cm represents that for 100 ${\text{c}}{{\text{m}}^2}$ of the curved surface area, the cost of white washing is Rs 12.5 which means that for 1 ${\text{c}}{{\text{m}}^2}$ of the curved surface area, the cost of white washing is Rs $\dfrac{{{\text{12}}{\text{.5}}}}{{100}}$ and then for 62800 ${\text{c}}{{\text{m}}^2}$of curved surface area, the cost of white washing will be Rs $\left( {\dfrac{{{\text{12}}{\text{.5}}}}{{100}}} \right) \times 62800$.