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Q15:

Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take $\pi = 3.14$)

Solution :

Initial Setup & Given Variables

Based on the standard geometric configuration of this problem, the figure consists of two concentric circles (circles sharing the same center point). The parameters provided are:

  • Radius of the outer circle, $R = 19 \text{ m}$
  • Width of the circular track (the radial distance between the inner and outer circles), $w = 10 \text{ m}$
  • The constant Pi, $\pi = 3.14$
O 19 m 9 m 10 m

Step 1: Calculation of the Outer Circle's Circumference

The circumference $C$ of any circle is given by the formula $C = 2\pi r$, where $r$ is the radius. [Per the fundamental geometric definition of a circle's perimeter].

For the outer circle, we substitute the given outer radius $R = 19 \text{ m}$:

$C_{\text{outer}} = 2 \pi R$
$C_{\text{outer}} = 2 \times 3.14 \times 19$
$C_{\text{outer}} = 6.28 \times 19$
$C_{\text{outer}} = 119.32 \text{ m}$

Step 2: Determination of the Inner Circle's Radius

The inner circle and the outer circle are concentric. The radius of the inner circle $r$ can be found by subtracting the width of the track from the radius of the outer circle $R$. [By the spatial properties of concentric circles].

$r = R - w$
$r = 19 \text{ m} - 10 \text{ m}$
$r = 9 \text{ m}$

Step 3: Calculation of the Inner Circle's Circumference

Using the derived inner radius $r = 9 \text{ m}$, we apply the circumference formula again for the inner circle:

$C_{\text{inner}} = 2 \pi r$
$C_{\text{inner}} = 2 \times 3.14 \times 9$
$C_{\text{inner}} = 6.28 \times 9$
$C_{\text{inner}} = 56.52 \text{ m}$

Final Summary

Final Solution: The circumference of the outer circle is $119.32 \text{ m}$ and the circumference of the inner circle is $56.52 \text{ m}$.


More Questions from Class 9 Mathematics Coordinate Geometry EXERCISE 9.2


CBSE Solutions for Class 9 Mathematics Coordinate Geometry


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