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In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region

Solution:

Given, arcs are drawn with radii 14 cm each with centres P, Q and R.

We have to find the area of the shaded region.

Here, radius = 14 cm

Area of sector = πr²θ/360°

θ₁ + θ₂ + θ₃ = 180°

Therefore area of shaded region = πr₁²θ₁/360° + πr₂²θ₂/360° + πr₃²θ₃/360°

Where r₁ = r₂ = r₃ = 14

area of shaded region = πr²/360° ( θ₁ + θ₂ + θ₃)

= (22/7)(14)²(180°/360°)

= (22)(2)(14)(1/2)

= (22)(14)

= 308 cm²

Area of shaded region = 308 cm²

Therefore, the area of the shaded region is 308 cm²

✦ Try This: A horse is tied to a pole at one corner of a square grass field of side 15 m using 10 m long rope. Find the area of that part of the field in which the horse can graze.

Given, square grass field of side 15 m

A horse is tied at one corner of the field using 10 m long rope.

We have to find the area of the field which the horse can gaze.

The area of field in which the cow gaze represents the area of a sector of a circle.

Here, radius = 10 m and corresponding angle, θ = 90°

Area of sector = πr²θ/360°

= (22/7)(10)²(90°/360°)

= (22/7)(100)(1/4)

= (22/7)(25)

= 78.57 square m

Therefore, the area of the field in which the horse can gaze is 78.57 square m.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.3 Problem 13

In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region

Summary:

In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. The area of the shaded region is 308 cm²

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