Question

How do you find the circumference and area of a circle with a diameter of 7cm?

Answer 1

Hint: Assume the diameter of the circle as ‘d’ and radius of the circle as ‘r’. Now, use the formula: - \[d=2r\] to find the value of radius of the circle. To find the circumference of this circle use the formula: - \[C=2\pi r\], where ‘C’ is the circumference. Now, to calculate the area, apply the relation: - \[A=\pi {{r}^{2}}\], where ‘A’ is the area. Substitute the value \[\pi =\dfrac{22}{7}\] to get the answer in whole numbers.

Complete step by step answer:
Here, we have been provided with the diameter of a circle and we are asked to determine the circumference and area of the circle.
Now, let us draw a rough diagram of the given circle.

In the above figure we have considered a circle with centre O and diameter AB whose length is 7cm. Let us denote the diameter with ‘d’ and radius with ‘r’. So, using the relation: - \[d=2r\], we have,
\[\Rightarrow r=\dfrac{d}{2}\]
Substituting the value of d = 7cm, we get,
\[\Rightarrow r=\dfrac{7}{2}\]cm
Now, let us find the circumference of this circle. Circumference of a circle can also be called as its perimeter and it is the length of the boundary of the circle. So, applying the formula for the circumference of the circle given as: - \[C=2\pi r\], where ‘C’ denotes the circumference, we get,
\[\Rightarrow C=2\pi \times \dfrac{7}{2}\]
Substituting the value \[\pi =\dfrac{22}{7}\], we get,
\[\Rightarrow C=2\times \dfrac{22}{7}\times \dfrac{7}{2}\]
\[\Rightarrow C=22\]cm
Now, let us find the area of the circle. We know that area of a circle is given as: - \[A=\pi {{r}^{2}}\], where ‘A’ is the area, so using the formula, we get,
\[\begin{align}
  & \Rightarrow A=\pi \times {{\left( \dfrac{7}{2} \right)}^{2}} \\
 & \Rightarrow A=\dfrac{22}{7}\times \dfrac{49}{4} \\
\end{align}\]
\[\Rightarrow \] Area = 38.5 \[c{{m}^{2}}\]
Hence, the circumference and area of the circle are 22cm and 38.5\[c{{m}^{2}}\] respectively.

Note:
One may note that here we were not provided with the value of \[\pi \] in the question but we considered it equal to \[\dfrac{22}{7}\] to make our calculation easy. You may take its value equal to 3.14. It will not make much difference to our answer. Do not forget to mention the units of circumference and area in the end otherwise it will be considered as an incomplete answer. Remember the formulas for the basic 2 – D shapes like: - square, triangle, rectangle etc.