Question

Find the circumference and area of a circle of diameter \[56m\].

Answer 1

Hint: We can find the radius of the circle using the diameter given. Radius is half the diameter. Using the radius, we can find the circumference and area of the circle.

Formula used: For a circle of radius $r$,
Circumference, $C = 2\pi r$
Area, $A = \pi {r^2}$
We can take an approximation of $\dfrac{{22}}{7}$ for $\pi $.

Complete step-by-step answer:
Given that the circle has diameter $56m$.
Since diameter is two times the radius, we have $radius,r = \dfrac{{diameter}}{2}$
So we have, $r = \dfrac{{56}}{2} = 28$
Therefore the radius of the circle is $28m$.
Now we can find the circumference.
For a circle of radius $r$,
Circumference, $C = 2\pi r$
Substituting we get,
Circumference, $C = 2 \times \pi \times 28 = 56\pi $
We can take an approximation of $\dfrac{{22}}{7}$ for $\pi $.
This gives, Circumference, $C = 56 \times \dfrac{{22}}{7} = 8 \times 22 = 176$
Therefore the circumference of the circle is $176m$.

Now we can find the area of the circle.
For a circle of radius $r$,
Area, $A = \pi {r^2}$
Substituting we get,
Area, $A = \pi \times {28^2}$
$ \Rightarrow Area,A = 784\pi $
We can take an approximation of $\dfrac{{22}}{7}$ for $\pi $.
So, we have, $ \Rightarrow Area,A = 784 \times \dfrac{{22}}{7} = 112 \times 22 = 2464$
Therefore, the area of the circle is $2464m$.

Note: Circumference of a circle is also called perimeter. The value of $\pi $ is obtained by dividing the circumference of a circle by its diameter. Its fractional approximation is $\dfrac{{22}}{7}$ and decimal approximation is $3.14$.