Question

The diameter of a roller 1meter long is 70cm. If it takes 200 revolutions to level a playground, find the cost of leveling at the rate of 75 paisa per meter square.

Answer 1

Hint: Here, in this given question, the roller is of the form of a cylinder whose diameter is 70cm and height or length is 1 meter. We can find its CSA (Curved Surface Area) as it is the area covered in 1 revolution and then we may multiply it by 200 to get the total area leveled by the roller. Thereafter, we multiply the product by 75 paisa to get the cost of leveling the whole playground.

Complete step-by-step answer:
In this given question, we are given that the diameter of a roller 1meter long is 70cm.
We are asked to find the cost at the rate of 75 paisa per meter square if it takes 200 revolutions to level a playground.
Now, as the roller is in the form of a cylinder, its diameter is 70cm and height or length is 1 meter or 100cm.

Curved Surface Area (CSA) of the cylinder is equal to$2\pi rh$ .
Putting the values, we get the CSA of the roller as
$\begin{align}
  & 2\pi rh=2\times \dfrac{22}{7}\times \dfrac{70}{2}\times 100 \\
 & =22000c{{m}^{2}} \\
\end{align}$
As it takes, 200 revolutions to level the whole field, the area of the field is equal to
$CSA\times 200=22000\times 200=4400000c{{m}^{2}}=440{{m}^{2}}$
As, the cost is 75 paisa per meter square, we get the total cost as
$440{{m}^{2}}\times 75=33000paisa$
As 1 rupee is equal to 100 paisa, 33000 paisa is equal to 330 rupees.
Therefore, we get the total cost of leveling the field as 330 rupees.

Note: Here, we must be careful while converting units as\[1m=100cm\] , \[1{{m}^{2}}=\text{ }10000c{{m}^{2}}\] and \[1rupee=100paisa.\]. It is also very important to remember all the formulas of respective shapes and students should be able to find the volume and CSA of a combination of solids also using these formulas.