Question

An oil drum is in the shape of a cylinder having the following dimensions : diameter is 2m and height is 7m. The painter charges Rs.3 per $m^2$ to paint the drum. Find the total charges to be paid to the painter for 10 drums?

Answer 1

Hint: In this question, we first need to find the total surface area of the cylinder with the given dimensions. Then find the charge to paint the total surface area which gives the charge for one drum. Now, multiply the charge for 1 drum with 10 to get the charges to be paid for 10 drums.Total surface area of the cylinder is given by \[\Rightarrow A=2\pi r\left( r+h \right)\].

Complete step-by-step answer:
Now, from the given question we have diameter as 2m and height 7m
Let us assume the height of the cylinder as h and radius as r
Now, from the given conditions we have
\[\Rightarrow h=7\]
As we already know the relation between radius and diameter we get,
\[\Rightarrow r=\dfrac{d}{2}\]
Now, on substituting the value of diameter we get,
\[\begin{align}
  & \Rightarrow r=\dfrac{2}{2} \\
 & \therefore r=1 \\
\end{align}\]
Let us assume the total surface area of the cylinder as A

As we already know that the formula for total surface area is given by
\[\Rightarrow A=2\pi r\left( r+h \right)\]
Let us now substitute the respective values in the above formula to get the total surface area of the cylinder
\[\Rightarrow h=7,r=1\]
Now, on substituting these values in the formula we get,
\[\Rightarrow A=2\pi \times 1\times \left( 1+7 \right)\]
Now, on further simplification we get,
\[\Rightarrow A=2\times \dfrac{22}{7}\times 8\]
Now, on simplifying this we get,
\[\therefore A=\dfrac{352}{7}{{m}^{2}}\]
Now, as given in the question that charge to paint per $m^2$ is Rs.3
Now, the charge to paint the total surface area of the cylinder is given by
\[\Rightarrow \dfrac{352}{7}\times 3\]
Now, on further simplification we get,
\[\Rightarrow Rs.\dfrac{1056}{7}\]
Now, as we got the charge for 1 drum we can get the charge for 10 drums as
\[\Rightarrow \dfrac{1056}{7}\times 10\]
Now, on further simplification we get,
\[\Rightarrow Rs.1058.57\]
Hence, the total charge to be paid for 10 drums is Rs. 1058.57

Note: Instead of finding the charge for 1 drum and then multiplying by 10 to get the total charge we can also directly get it by finding the area of 10 drums and then find the cost accordingly. Both the methods give the same result.It is important to note that we need to find the cost of each drum after finding the area and then multiply with 10 because neglecting any of the steps changes the result.