Question

What is the circumference and the area of a circle that has a diameter of \[35\]cm?

Answer 1

Hint: Let us consider the diameter of a circle is \[2r\].
We know that the radius of a circle is half of the diameter.
So, the radius of the circle is \[r\].
The circumference of a circle with radius \[r\ ]is \[2\pi r\] and the area of the circle is \[\pi {r^2}\].

Complete step-by-step solution:
It is given that the diameter of the circle is \[35\]cm.
We have to find the circumference and the area of the given circle.
To find the circumference and the area we have to find the radius of the circle.
We know that the radius of a circle is half of the diameter.
The radius of the circle is \[\dfrac{{35}}{2} = 17.5\] cm.
We know that the circumference of a circle with radius \[r\]is \[2\pi r\].
Again, the area of the circle with radius \[r\]is \[\pi {r^2}\].
Now, substitute the value of \[r = 17.5\] cm in the given formula we get,
The circumference is \[2 \times \dfrac{{22}}{7} \times 17.5\] cm
Simplifying we get,
The circumference is \[110\]cm.
Again, substitute the value of \[r = 17.5\] cm in the given formula we get,
The area is \[\dfrac{{22}}{7} \times {17.5^2}\] sq. cm
Simplifying we get,
The circumference is \[962.5\]sq. cm.
Hence, the circumference of the circle is \[110\]cm and the area is \[962.5\]sq. cm.

Note: In Mathematics, the circumference of any shape defines the path or the boundary that surrounds the shape. In other words, the circumference is also called the perimeter, which helps to identify the length of the outline of any shape.
Area of any circle is the region enclosed by the circle itself or the space covered by the circle.
The circumference of a circle with radius \[r\] is \[2\pi r\].
The area of the circle with radius \[r\] is \[\pi {r^2}\].