To find the cost of making the designs on a round table cover with six equal designs:
Area of One Design: The table cover is divided into six equal parts, each part being a sector of the circle. The area of a sector is given by (θ/360)×πr², where θ is the angle of the sector and r is the radius. Since there are six designs, each sector has an angle of 360°/6 = 60°. With r = 28 cm, the area of one design is (60/360)×π×28² cm².
Total Area for Six Designs: Multiply the area of one design by six.
Cost Calculation: Multiply the total area by the cost per cm², ₹0.35.
The final calculation gives the total cost of making the designs on the table cover.

Let’s discuss in detail

## Crafting Designs on a Round Table Cover

The task of calculating the cost of making designs on a round table cover is a practical application of geometry in the realm of textile design and craftsmanship. In this scenario, a round table cover, with a radius of 28 cm, features six equal designs. Each design is a sector of the circle that forms the table cover. The cost of crafting these designs is determined by the area they cover and the rate charged per square centimeter. This problem not only involves geometric calculations but also reflects the intersection of art, design, and mathematics.

### Geometric Division of the Table Cover

The round table cover is divided into six equal parts for the designs. This division implies that each design occupies a sector of the circle. The angle of each sector in a circle is determined by dividing the total angle of the circle (360 degrees) by the number of sectors. Since there are six designs, each sector has an angle of (360°/6) = 60°. This division is crucial for calculating the area that each design will occupy on the table cover.

#### Calculating the Area of a Single Design

To calculate the area of one design, we use the formula for the area of a sector: (θ/360)×πr², where θ is the angle of the sector, and r is the radius of the circle. With a radius of 28 cm and a sector angle of 60°, the area of one design is (60/360)×π×28² square centimeters. This calculation gives us the area occupied by one of the six designs on the table cover.

Total Area Covered by All Designs
After calculating the area of one design, the next step is to determine the total area covered by all six designs. This is simply six times the area of one design, as all designs are equal. The total area for the six designs is 6×(60/360)×π×28² square centimeters. This total area is essential for calculating the overall cost of making the designs on the table cover.

##### Cost Calculation for the Designs

The cost of making the designs is calculated by multiplying the total area covered by the designs by the rate charged per square centimeter. Given the rate is ₹0.35 per square centimeter, the total cost is the product of this rate and the total area calculated in the previous step. This step translates the geometric calculation into a monetary value, providing the total cost for crafting the designs on the table cover.

###### The Intersection of Geometry and Craftsmanship

In conclusion, this problem illustrates the practical application of geometry in textile design and craftsmanship. By calculating the area of each design and subsequently the total area for all designs, we can determine the cost of creating these patterns on a round table cover. This exercise not only highlights the importance of geometry in design and manufacturing but also shows how mathematical concepts are integral in various aspects of practical life, including crafting and economics. It’s a fascinating example of how geometry aids in bridging creativity with practicality.

Discuss this question in detail or visit to Class 10 Maths Chapter 11 for all questions.
Questions of 10th Maths Exercise 11.1 in Detail

 Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. Find the area of a quadrant of a circle whose circumference is 22 cm. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding (i) minor segment (ii) major sector. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors. Find (i) the total length of the silver wire required. (ii) the area of each sector of the brooch. An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. A round table cover has six equal designs. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per cm².

Last Edited: June 11, 2024