Question

Find the diameter, circumference and area of the circle having radius 6.5?

Answer 1

Hint: we know that diameter is double of the radius. The formula for circumference of the circle is given by $C = 2\pi r$. The formula for area of the circle is given by $Area = \pi {r^2}$ where r is the radius of the circle and C is the circumference.

Complete step-by-step solution:
The circumference of a circle is equal to its perimeter in geometry. That is, the circumference of the circle will be equal to its arc length, as if it were opened up and straightened out to a line segment. In general, the perimeter is the length of any closed figure's curve. As the number of sides increases without restriction, the circumference of a circle can be defined as the limit of the perimeters of inscribed regular polygons. The circumference of a circle is the length of the circle's boundary. When measuring physical objects and considering abstract geometric forms, the term circumference is utilized.

We have given radius of the circle which is 6.5unit
We know that diameter of the circle is double of the radius
So, diameter $ = 2r$
Diameter $ = 2 \times 6.5$
Diameter $ = 13 \text{unit}$
We know that the formula for circumference of the circle is given by $C = 2\pi r$
So,
$C = 2\pi r$
We have put the value of radius
$C = 2 \times \pi \times 6.5$
$\Rightarrow C = 2 \times 3.14 \times 6.5$
$\Rightarrow C = 40.82 \text{unit}$
we know that the formula for area of the circle is given by $Area = \pi {r^2}$
$Area = \pi {r^2}$
We have put the value of the radius
$\text{Area} = \pi \times {6.5^2}$
$\Rightarrow \text{Area} = 3.14 \times {6.5^2}$
$\Rightarrow \text{Area} = 132.665 \text{unit}^{2}$
The diameter, circumference and the area of the circle having radius 6.5 is 13, 40.82 and 132.665 respectively.

Note: The definitions and formulas for determining the circumference and area of a circle should be remembered by students. If the radius of a circle is given in terms of diameter, we must convert it to radius using the relationship \[Radius = \dfrac{{Diameter}}{2}\] before calculating the circumference of the circle or the straight formula \[C = \pi \times d\] can be used. To avoid making mistakes, the computations must be done carefully.