Geometry - Introduction to Circles

If the radius of a circular plate is $6$ cm, find the length of its diameter.

Given: Radius ($r$) = $6$ cm. We know that $Diameter (d) = 2 \times Radius (r)$. $d = 2 \times 6$ $d = 12$ cm.

Since the diameter of a circle is twice the length of its radius, we multiply the given radius of $6$ cm by $2$ to find that the diameter is $12$ cm.

The diameter of a bicycle wheel is $50$ cm. What is the radius of the wheel?

Given: Diameter ($d$) = $50$ cm. We know that $Radius (r) = \frac{Diameter (d)}{2}$. $r = \frac{50}{2}$ $r = 25$ cm.

To find the radius when the diameter is known, we divide the diameter by $2$. Dividing $50$ cm by $2$ gives us a radius of $25$ cm.

$Diameter = 2 \times Radius$ $Diameter = 2 \times 14 \text{ cm}$ $Diameter = 28 \text{ cm}$

To find the diameter, we use the relationship that the diameter is exactly twice the length of the radius. Multiplying $14$ cm by $2$ gives $28$ cm.

$Radius = \frac{Diameter}{2}$ $Radius = \frac{44 \text{ cm}}{2}$ $Radius = 22 \text{ cm}$

The radius is half the length of the diameter. Dividing the total length of the diameter ($44$ cm) by $2$ results in a radius of $22$ cm.