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

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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