An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella
![An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/12-2-17-1563259215.png)
Solution:
We will use the concepts related to the area of a sector of a circle to solve the problem.
There are 8 equally spaced ribs in an umbrella, so the umbrella is assumed to be a flat circle.
∴ The angle between 2 consecutive ribs (θ) = 360°/8 = 45°
The radius of the flat circle (r) is given as 45 cm.
The area between 2 consecutive ribs of the umbrella = Area of a sector with an angle of 45° = θ/360° × πr2
= 45°/360° × 22/7 × 45 cm × 45 cm
= 1/8 × 22/7 × 45 cm × 45 cm
= 22275/28 cm2
= 795.535 cm2
☛ Check: Class 10 Maths NCERT Solutions Chapter 12
Video Solution:
An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 10
Summary:
An umbrella has 8 ribs which are equally spaced as shown in the figure. Assuming umbrella to be a flat circle of radius 45 cm, the area between the two consecutive ribs of the umbrella is 795.535 cm2.
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