Find the area of the square field excluding the lawn. Rani bought a new field that is next to one she already owns (Fig. 9.34). This field is in the shape of a square of 70 m. She makes a semi circular lawn of maximum area in this field.
Solution:
Given, Rani bought a new field that is next to one she already owns.
The new field is in the shape of a square of 70 m.
She makes a semicircular lawn of maximum area in this field.
We have to find the area of the square field excluding the lawn.
The side of the square will be the diameter of a semicircle.
Diameter = 70 m
Radius, r = 70/2 = 35 m
Area of semicircle = 1/2 × πr²
= 1/2 × 22/7 × (35)²
= 11 × 5 × 35
= 55 × 35
= 1925 m²
Area of square = (side)²
= (70)²
= 4900 m²
Area of the square field excluding the lawn = area of square - area of semicircle
= 4900 - 1925
= 2975 m²
Therefore, the required area is 2975 m².
✦ Try This: Rama bought a new field that is next to one she already owns (Fig. 9.34). This field is in the shape of a square of 80 m. She makes a semi circular lawn of maximum area in this field. Find the area of the square field excluding the lawn.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 80(ii)
Find the area of the square field excluding the lawn. Rani bought a new field that is next to one she already owns (Fig. 9.34). This field is in the shape of a square of 70 m. She makes a semi circular lawn of maximum area in this field.
Summary:
Rani bought a new field that is next to one she already owns (Fig. 9.34). This field is in the shape of a square of 70 m. She makes a semi circular lawn of maximum area in this field. The area of the square field excluding the lawn is 2975 m²
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