Question

The diameter of a circular plate is \[28cm\]. Find the diameter of that circular plate whose area is half of this plate.

Answer 1

Hint: Here, in the given question, a circular plate is given whose diameter is\[28cm\]and we are asked to find the diameter of another circular plate whose area is half of the area of the given plate. To find the required diameter, at first we will calculate the area of the given plate and then compare it with the area of another plate. By doing this we will get the radius and hence the required diameter of another plate.
Formula used:
Area of the circle is calculated by\[\pi {r^2}\], where \[r\]is the radius of the circle.

Complete step-by-step solution:
Given, diameter of a circular plate= \[28cm\]
Therefore, radius of a circular plate= \[14cm\] [\[\because \]Diameter= \[2\]times radius]
Then, Area of given circular plate= \[\pi {\left( {14} \right)^2}c{m^2}\] [\[\because \]Area of circle=\[\pi {r^2}\]]
Now, it is given that the area of another plate is half of the area of the given plate.
Therefore, Area of required plate=\[\dfrac{1}{2}\pi {\left( {14} \right)^2}c{m^2}\]
\[ \Rightarrow \]Area of required plate=\[\pi {\left( {\dfrac{{14}}{{\sqrt 2 }}} \right)^2}c{m^2}\]
On comparing it with the formula of area or circle, we get,
Required radius of plate=\[\dfrac{{14}}{{\sqrt 2 }}cm\]
Hence, the required diameter=\[2 \times \dfrac{{14}}{{\sqrt 2 }}cm\]
\[ = 14\sqrt 2 cm\]

Note: The area of a circle is the space or the region occupied inside the circle. In mathematical terms, we can say that the area of a circle is the total number of square units inside the circle. Such type of questions are very easy as we need only one measurement i.e. radius/diameter to solve most of the questions related to circle.
Observe what is asked in the question and move accordingly. There is no need to complicate calculations. Put the value of\[\pi \]if required only.