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In a school, exactly at the middle of the stage of the assembly hall, after drawing a circle of \[2.8\]m radius, a beautiful picture is to be drawn in it. Cost for drawing is Rs.\[300\] per \[1\]sq. m. What is the total cost (in Rs) of drawing a picture in this circle?

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Last updated date: 22nd Jun 2024
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Answer
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Hint: In this question, we have to find the total cost of drawing a picture in this circle.
First we need to find out the area of the circle, then by unitary method we will get the total cost of drawing a picture in this circle from the given information.

Formula used: The area of a circle is \[\pi {r^2}\]sq. unit. Where the radius of the circle is r.

Complete step-by-step answer:
It is given that, in a school, exactly at the middle of the stage of the assembly hall, after drawing a circle of \[2.8\]m radius, a beautiful picture is to draw in it.
Also given that, the cost for drawing is Rs\[300\] per \[1\]sq. m.
We have the radius of the circle is r = \[2.8\]m.
We know that the area of the circle is \[\pi {r^2}\]
By substituting the value of r we get,
\[\pi {r^2} = \dfrac{{22}}{7} \times {\left( {2.8} \right)^2}\]
By cancelling the cancellable terms we get,
\[\pi {r^2} = 22 \times 2.8 \times 0.4\]
On solving we get,
\[\pi {r^2} = 24.64\]Sq. m.
Thus the area of the circle is \[\pi {r^2} = 24.64\]Sq. m.
From given we have the cost of drawing \[1\] sq. m. is Rs\[300\].
Then the cost of drawing \[24.64\] sq. m. is Rs. \[24.64 \times 300 = 7392\]

Hence the total cost of drawing a picture in this circle is Rs. \[7392\].

Note: We have solved the problem by unitary method.
Now we need to know what unitary method is.
In short, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.
For simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side.
Using the given radius we will find the area of the circle. Here we have to find the area of the circle because while finding the area we will get the result in square units that is the total surface covered by the circle is found which will help us to find the exact value of the drawing.