Question

The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.

Answer 1

Hint: Circumference of the circle is given as \[2\Pi r\], where r= radius of the circle. According to the given condition form equation and solve.

Complete step-by-step answer:

Given, the circumference of a circle exceeds the diameter by 16.8 cm.
Let diameter of the circle (D) =x cm
\[ \Rightarrow \]Radius of the circle (r)\[ = \dfrac{D}{2} = \dfrac{x}{2}cm\]
Mathematically,
 \[ \Rightarrow 2\Pi r = x + 16.8 \\
   \Rightarrow \Pi (2r) = x + 16.8 \\
   \Rightarrow \Pi x = x + 16.8 \\
   \Rightarrow \Pi x - x = 16.8 \\
   \Rightarrow (\Pi - 1)x = 16.8 \\
   \Rightarrow \left[ {\dfrac{{22}}{7} - 1} \right]x = 16.8 \\
   \Rightarrow \left[ {\dfrac{{15}}{7}} \right]x = 16.8 \\
   \Rightarrow x = 7.84 \\
\]
Diameter of the circle (D)=x cm=7.84 cm
Radius of the circle (r)= \[ = \dfrac{D}{2} = \dfrac{x}{2}cm\]=\[\dfrac{{7.84}}{2} = 3.92cm\].

Note: The diameter is the length of the line through the centre that touches two points on the edge of the circle. Circumference of the circle can also be given as \[Diameter \times \Pi \].