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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 $\pi = 3.14$)
Solution :
Step 1: Given Variables & Initial Setup
To determine the length and cost of the lace required for the circular table cover, we first extract the given geometric and financial parameters:
- Diameter of the circular table cover ($d$): $1.5 \text{ m}$
- Radius of the circular table cover ($r$): $r = \frac{d}{2} = \frac{1.5}{2} = 0.75 \text{ m}$
- Cost of lace per meter: ₹ $15$
- Value of Pi ($\pi$): $3.14$ [As explicitly specified in the problem constraints]
Step 2: Geometric Visualization
The lace is to be attached to the outer edge of the circular table cover. In Euclidean geometry, the continuous line forming the boundary of a closed geometric figure is its perimeter. For a circle, this boundary is defined as the circumference.
Step 3: Calculating the Length of the Lace Required
The total length of the lace required is mathematically equivalent to the circumference of the circle. [Per the geometric definition of a circle's perimeter, $C = \pi d$ or $C = 2\pi r$].
Using the diameter formula for circumference:
$C = \pi \times d$
Substituting the given values into the equation:
$C = 3.14 \times 1.5 \text{ m}$
Performing the arithmetic multiplication:
$C = 4.71 \text{ m}$
Therefore, the exact length of the lace required to cover the edge of the table is $4.71 \text{ m}$.
Step 4: Calculating the Total Cost of the Lace
The total financial cost is determined by taking the product of the total length of the lace and the unit cost per meter. [By the principle of linear proportionality in unit pricing].
$\text{Total Cost} = \text{Total Length of Lace} \times \text{Cost per meter}$
Substituting the calculated length and the given rate:
$\text{Total Cost} = 4.71 \text{ m} \times 15 \text{ ₹/m}$
Breaking down the multiplication for precision:
- $4.71 \times 10 = 47.10$
- $4.71 \times 5 = 23.55$
- $47.10 + 23.55 = 70.65$
$\text{Total Cost} = 70.65 \text{ ₹}$
Final Solution: The total length of the lace required to cover the edge of the circular table is $4.71 \text{ m}$, and the total cost to purchase this lace is ₹ $70.65$.
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 $\pi = 3.14$)
- Q15: Find the circumference of the inner and the outer circles, shown in the adjoining figure? (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 $\pi = 3.14$)
- 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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