Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.
Solution:
The diagram below shows the areas grazed by the four horses tethered at the four corners of the square ground.
Area grazed by the horses is represented by areas 1, 2, 3, and 4. The radius of the four curves is 35 m.
The four areas 1, 2, 3, and 4 are:
A = πr²/4 + πr²/4 + πr²/4 + πr²/4
A = πr²
A = (22/7) × (35)²
A = (22/7) × 35 × 35
A = 3850m²
Total Area of the square field = 70² = 4900m²
Area left ungrazed(5)= 4900m² - 3850 m² = 1050m²
✦ Try This: Four horses are tethered with equal ropes at 4 corners of a square field of side 84 metres so that they just can reach one another. Find the area left ungrazed by the horses.
Area grazed by the horses is represented by areas 1, 2, 3, and 4. The radius of the four curves is 40 m.
The four areas 1, 2, 3, and 4 are:
A = πr²/4 + πr²/4 + πr²/4 + πr²/4
A = πr²
A = (22/7) × (42)²
A = (22/7) × 42 × 42
A = 5544m²
Total Area of the square field = 84² = 7056m²
Area left ungrazed(5) = 7056m² - 5544 m² = 1512m²
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 64
Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.
Summary:
Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. The area left ungrazed by the horses is 1050 m²
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