Question

The circumference of a circle is 97.2 cm. Find its diameter and radius.

Answer 1

Hint:
Here, we have to use the concept of circumference to find the diameter of the circle. Circumference of the circle is the length of the outer boundary of the circle. So, by simply equating the circumference of the circle to the given value i.e. 97.2 cm we will get the value of the diameter of the circle and radius of the circle.

Complete step by step solution:
Let d be the diameter of the circle and r be the radius of the circle.
Value of \[{\rm{\pi }}\] is 3.14
It is given that circumference of the circle is 97.2 cm
Therefore, circumference of the circle\[{\rm{ = \pi d = 97}}{\rm{.2}}\]
So, by solving the above equation we will get the value of the diameter of the circle.
\[{\rm{d = }}\dfrac{{{\rm{97}}{\rm{.2}}}}{{\rm{\pi }}}{\rm{ = }}\dfrac{{{\rm{97}}{\rm{.2}}}}{{{\rm{3}}{\rm{.14}}}}{\rm{ = 30}}{\rm{.93 cm}}\]
So, the diameter of the circle is 30.93 cm.
We know that the radius of the circle is equal to the half of the diameter of the circle.
Therefore, radius of the circle, r \[{\rm{ = }}\dfrac{{\rm{d}}}{2} = \dfrac{{{\rm{30}}{\rm{.93}}}}{2}{\rm{ = 15}}{\rm{.46 cm}}\]

Hence, 30.93 cm is the diameter of the circle and 15.46 cm is the radius of the circle.

Note:
We should know that circumference is the similar concept as the perimeter of the shapes and both are generally measured in a single unit i.e. centimetre or meter. Area is the amount of surface covered by a shape in two dimensions. Area is generally measured in square units.
Area of the circle\[{\rm{ = }}\dfrac{{{\rm{\pi }}{{\rm{d}}^2}}}{4}\], where d is the diameter of the circle.
Diameter of a circle is equal to two times the radius of the circle.
It is important to write the units of measurement with the values.