Question

What will be the cost of painting for the circular roof of a building of radius $4.2m$ at the rate of $Rs\,25$ per square metre?

Answer 1

Hint: In this question we have to find the cost of painting the circular roof, so we will first need to calculate the area of the circular roof.
We know the formula of circle i.e. $\pi {r^2}$ , where
$r$ is the radius, which is given in the question $r = 4.2m$ .
 After this we will multiply the area with the given cot of costing and we will get our answer.

Complete step by step solution:
We have to find what will be the cost to paint the circular roof of a building with the given radius at the rate of $Rs\,25$ per square metre.
So we know the radius of circular roof i.e.
 $r = 4.2m$
By applying the formula we can calculate the area of the circular roof
$\Rightarrow$ $\pi \times {(4.2)^2}$
We will simplify the value i.e.
$\Rightarrow$ $\dfrac{{22}}{7} \times \dfrac{{42}}{{10}} \times \dfrac{{42}}{{10}}$
On further solving we have :
$\Rightarrow$ $\dfrac{{33 \times 42}}{{25}}$
It gives us value
$\Rightarrow$ $\dfrac{{1386}}{{25}}{m^2}$
Now we will multiply the area with the rate per square metre:
$\Rightarrow$ $Rs\,\left( {\dfrac{{1386}}{{25}} \times 25} \right)$
So it gives us value
$\Rightarrow$ $Rs\,1386$ .
Hence the required total cost of painting is $Rs\,1386$
So, the correct answer is “Option B”.

Note: We should note that in these types of questions, we should always know the basic mensuration formulas beforehand. If in the above question, we have been given the diameter of a circular roof, instead of radius, then we can calculate the radius by dividing the diameter with $2$,
 it can be written as
$r = \dfrac{d}{2}$ .
We should also always check for the units, in which the question is asking the answer.