NCERT Class X Chapter 11: Area Related To Circles Exercise 11.1 Question 10

NCERT Class X Chapter 11: Area Related To Circles

Question:

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.

Given:

Number of ribs \( = 8 \)
Radius of the umbrella \( r = 45\, \text{cm} \)

To Find:

Area between two consecutive ribs of the umbrella.

Formula:

Area of a circle:   \( A = \pi r^2 \)
Area between two consecutive ribs:   \( \dfrac{\text{Area of circle}}{\text{Number of ribs}} \)

Solution:

Step 1: Write the formula for the area of the umbrella (circle).

$$ \text{Area of umbrella} = \pi r^2 $$

Step 2: Substitute the value of \( r = 45\, \text{cm} \).

$$ \text{Area} = \pi \times (45)^2 = \pi \times 2025 = 2025\pi\ \text{cm}^2 $$

Step 3: Find the area between two consecutive ribs.

$$ \text{Area between two ribs} = \frac{2025\pi}{8}\ \text{cm}^2 $$

Step 4: Calculate the value using \( \pi = \frac{22}{7} \).

$$ \text{Area} = \frac{2025 \times \frac{22}{7}}{8} = \frac{2025 \times 22}{7 \times 8} = \frac{44550}{56} \approx 795.21\, \text{cm}^2 $$

Result:

The area between two consecutive ribs of the umbrella is approximately \( 795.21\, \text{cm}^2 \).

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