NCERT Class X Chapter 11: Area Related To Circles Exercise 11.1 Question 13
NCERT Class X Chapter 12: Areas Related to Circles
Question:
A round table cover has six equal designs as shown in Fig. 11.11. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2. (Use \( \sqrt{3} = 1.7 \))
Given:
Radius of the circular table cover, \( r = 28 \) cm
Number of designs = 6
Rate of making designs = ₹ 0.35 per cm2
\( \sqrt{3} = 1.7 \)
To Find:
Cost of making the six designs on the table cover
Formula:
Area of a circle: $$ A = \pi r^2 $$ Area of a regular hexagon of side \( a \): $$ A = \frac{3\sqrt{3}}{2} a^2 $$
Solution:
Step 1: The six designs together form the region between the circular table cover and the regular hexagon inscribed in it.
Step 2: Find the area of the circular table cover.
$$ A_{\text{circle}} = \pi r^2 = \frac{22}{7} \times 28 \times 28 = 2464 \text{ cm}^2 $$Step 3: The side of the regular hexagon is equal to the radius of the circle.
$$ a = 28 \text{ cm} $$Step 4: Find the area of the regular hexagon.
$$ A_{\text{hexagon}} = \frac{3\sqrt{3}}{2} a^2 = \frac{3 \times 1.7}{2} \times 28^2 = 1999.2 \text{ cm}^2 $$Step 5: Find the total area of the six designs.
$$ A_{\text{designs}} = 2464 - 1999.2 = 464.8 \text{ cm}^2 $$Step 6: Calculate the cost of making the designs.
$$ \text{Cost} = 464.8 \times 0.35 = 162.68 $$Result:
The cost of making the six designs on the table cover is ₹ 162.68.
Comments
Post a Comment