Question

Ram has a plate in circular form which has a design in a $ 7 $ meter radius. Find the area in $ c{m^2} $ .

Answer 1

Hint: Here in this question we want to find the area of a circle and whose radius is given to us as $ 7 $ meters. To find the area we have the standard formula is $ A = \pi {r^2} $ . We know the value of $ \pi $ and the value of radius is given to us in the question itself. We substitute known values and determine the area of a circle using the formula. But we have to find the area in $ c{m^2} $ and the radius of the circle is given to us in the unit meters. So, we first convert the radius of the circle from the unit meters to centimetres and then put the value of radius in the formula for area of the circle.

Complete step by step solution:
The circle is a two dimensional figure and we have to determine the area, where the area is the region or space occupied by the circular field. To determine the area of a circle we have the standard formula $ A = \pi {r^2} $ where r represents the radius. The radius of a circle is the line segment which joins the centre of the circle to any point on the circle or to the circumference. The radius is denoted as ‘R’ or ‘r’. The unit for the area is square units. In the given question, we are given the length of the radius in meters. So, we first convert it into centimetres to get the area of the circle in centimetres square.
So, we have the radius of the circle as $ 7 $ meters.
We know that each metre of length consists of $ 100 $ centimetres.
So, let the number of centimetres that correspond to $ 7 $ metres be x. Then, to convert $ 7 $ metres into centimetres, we follow a unitary method.
So, $ 1 $ metre $ = $ $ 100 $ centimetres
Hence, $ 7 $ meters $ = $ $ 700 $ centimetres
Now, to find the area of a circle, we use formula $ A = \pi {r^2} $ . The radius of the circle is $ 700 $ centimetres.
By substituting, we get,
 $ A = \pi {r^2} $
 $ \Rightarrow A = \pi {\left( {700} \right)^2} $ square centimetres
Computing the square of the number, we get,
 $ \Rightarrow A = 490000\pi $ square centimetres
Substituting the value of $ \pi $ in the equation, we get,
 $ \Rightarrow A = 490000 \times \left( {\dfrac{{22}}{7}} \right) $ square centimetres
Cancelling the common factors in numerator and denominator, we get,
 $ \Rightarrow A = 70000 \times 22 $ square centimetres
Simplifying the calculations,
 $ \Rightarrow A = 1540000 $ square centimetres
Therefore the area of a circle with a radius $ 7 $ meter is $ 1540000 $ square centimetres.
So, the correct answer is “ $ 1540000 $ square centimetres.”.

Note: A circle is a closed two dimensional figure. Generally the area is the region occupied by the thing. The area of a circle is defined as the region occupied by the circular region. It can be determined by using formula $ A = \pi {r^2} $ where r is the radius of the circle. The radius is denoted by r or R. We must know how to convert the quantities from one unit to another. We must take care of the calculations in order to be sure of the final answer.