Question

How do you find the area of a circle with diameter 2 yd?

Answer 1

Hint: We have been given a circle along with the measurement of its diameter as 2 yards. We shall find the circumference of this circle using the formula $C=2\pi r$ and then we shall find the area of the circle using the formula $A=\pi {{r}^{2}}$. We must remember that the units of circumference and area are yards and square yards respectively.

Complete step by step solution:
A quantity related to a circle is its diameter which is a line which joins two opposite points on the circle. It has double the measurement of the radius of the circle.
$r=\dfrac{d}{2}$
Where,
$r=$ radius of circle
$d=$ diameter of circle
Given that, $d=2$yd
$\Rightarrow r=\dfrac{2}{2}$
$\Rightarrow r=1$yd
The circumference, $C$ of a circle is the measurement of the boundary of the circle or the perimeter of the circle. It is given as:
$C=2\pi r$
Putting the value of radius equal to 1 yd, we get
$\Rightarrow C=2\pi \left( 1 \right)$
$\Rightarrow C=2\pi $yards
The area, $A$ of a circle is the region enclosed by the circle in a two-dimensional plane. Area of the circle is given as:
$A=\pi {{r}^{2}}$
Substituting the value of radius equal to 1 yard, we get
$\Rightarrow A=\pi {{\left( 1 \right)}^{2}}$
$\Rightarrow A=\pi \left( 1 \right)$
$\Rightarrow A=\pi $ square yards
Therefore, for a circle with diameter 2 yard, the circumference is equal to $2\pi $yards and the area is equal to $\pi $square yards.

Note: A circle is defined as the locus off all points equidistant from a central point. This equal distance of all points from the central point is known as the radius of the circle and the central point is known as the center of the circle.