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Q15:
Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take $\pi = 3.14$)

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, $\pi = 3.14$
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
- Q1(a): Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (a) $14$ cm
- Q1(b): Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (b) $28$ mm
- Q1(c): Find the circumference of the circles with the following radius: (Take $\pi = \frac{22}{7}$) (c) $21$ cm
- Q10: From a circular card sheet of radius $14$ cm, two circles of radius $3.5$ cm and a rectangle of length $3$ cm and breadth $1$cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (Take $\pi = \frac{22}{7}$)
- Q11: A circle of radius $2$ cm is cut out from a square piece of an aluminium sheet of side $6$ cm. What is the area of the left over aluminium sheet? (Take $\pi = 3.14$)
- Q12: The circumference of a circle is $31.4$ cm. Find the radius and the area of the circle? (Take $\pi = 3.14$)
- Q13: A circular flower bed is surrounded by a path $4$ m wide. The diameter of the flower bed is $66$ m. What is the area of this path? ($\pi = 3.14$)
- Q14: A circular flower garden has an area of $314$ m$^2$. A sprinkler at the centre of the garden can cover an area that has a radius of $12$ m. Will the sprinkler water the entire garden? (Take $\pi = 3.14$)
- Q16: How many times a wheel of radius $28$ cm must rotate to go $352$ m? (Take $\pi = \frac{22}{7}$)
- Q17: The minute hand of a circular clock is $15$ cm long. How far does the tip of the minute hand move in $1$ hour. (Take $\pi = 3.14$)
- Q2(a): Find the area of the following circles, given that: (a) radius = $14$ mm (Take $\pi = \frac{22}{7}$)
- Q2(b): Find the area of the following circles, given that: (b) diameter = $49$ m
- Q2(c): Find the area of the following circles, given that: (c) radius = $5$ cm
- Q3: If the circumference of a circular sheet is $154$ m, find its radius. Also find the area of the sheet. (Take $\pi = \frac{22}{7}$)
- Q4: A gardener wants to fence a circular garden of diameter $21$ m. Find the length of the rope he needs to purchase, if he makes $2$ rounds of fence. Also find the cost of the rope, if it costs ₹ $4$ per meter. (Take $\pi = \frac{22}{7}$)
- Q5: From a circular sheet of radius $4$ cm, a circle of radius $3$ cm is removed. Find the area of the remaining sheet. (Take $\pi = 3.14$)
- Q6: Saima wants to put a lace on the edge of a circular table cover of diameter $1.5$ m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ $15$. (Take $\pi = 3.14$)
- Q7: Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
- Q8: Find the cost of polishing a circular table-top of diameter $1.6$ m, if the rate of polishing is ₹ $15/m^2$. (Take $\pi = 3.14$)
- Q9: Shazli took a wire of length $44$ cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take $\pi = \frac{22}{7}$)
CBSE Solutions for Class 9 Mathematics Coordinate Geometry
Chapters in CBSE - Class 9 Mathematics
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