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Four horses are tethered at four comers of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.
- a)42 m2
- b)22 m2
- c)84 m2
- d)168 m2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Four horses are tethered at four comers of a square plot of side 14 m ...
Total area of plot = 14 * 14 = 196m2
Horses can graze in quarter circle of radius = 7m
Grazed area = 4 * (pie r2)/4 = 154 m2
Area of plot when horses cannot reach = (196 - 154) = 42m2
Ungrazed area = 42 - 20 = 22m2
Horses can graze in quarter circle of radius = 7m
Grazed area = 4 * (pie r2)/4 = 154 m2
Area of plot when horses cannot reach = (196 - 154) = 42m2
Ungrazed area = 42 - 20 = 22m2
Most Upvoted Answer
Four horses are tethered at four comers of a square plot of side 14 m ...
Given information:
- Four horses are tethered at four corners of a square plot of side 14 m.
- Adjacent horses can just reach one another.
- There is a small circular pond of area 20 m² at the center.
To find:
The ungrazed area.
Solution:
Let's draw a diagram to visualize the given information.
We can see that the distance between adjacent horses is the radius of the circular pond.
Let the radius of the circular pond be r meters.
We know that the area of a circle is given by πr².
So, πr² = 20
r² = 20/π
r = √(20/π) = 2.52 m (approx.)
Now, let's find the area of the square plot.
The side of the square plot is 14 m.
So, the area of the square plot = 14² = 196 m².
The total area grazed by the horses is the area of four quarter circles with radius r each.
Area grazed by one horse = ¼ × πr² = ¼ × π × 2.52² = 5 m²
Total area grazed by four horses = 4 × 5 = 20 m².
Therefore, the ungrazed area = Total area - Grazed area
= 196 - 20
= 176 m².
Hence, the correct option is (b) 22 m².
Note: We can also find the ungrazed area by subtracting the area of four sectors of radius 14 m and central angle 90° each from the area of the square plot. The result will be the same.
- Four horses are tethered at four corners of a square plot of side 14 m.
- Adjacent horses can just reach one another.
- There is a small circular pond of area 20 m² at the center.
To find:
The ungrazed area.
Solution:
Let's draw a diagram to visualize the given information.
We can see that the distance between adjacent horses is the radius of the circular pond.
Let the radius of the circular pond be r meters.
We know that the area of a circle is given by πr².
So, πr² = 20
r² = 20/π
r = √(20/π) = 2.52 m (approx.)
Now, let's find the area of the square plot.
The side of the square plot is 14 m.
So, the area of the square plot = 14² = 196 m².
The total area grazed by the horses is the area of four quarter circles with radius r each.
Area grazed by one horse = ¼ × πr² = ¼ × π × 2.52² = 5 m²
Total area grazed by four horses = 4 × 5 = 20 m².
Therefore, the ungrazed area = Total area - Grazed area
= 196 - 20
= 176 m².
Hence, the correct option is (b) 22 m².
Note: We can also find the ungrazed area by subtracting the area of four sectors of radius 14 m and central angle 90° each from the area of the square plot. The result will be the same.
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Community Answer
Four horses are tethered at four comers of a square plot of side 14 m ...
Total area of plot = 14 * 14 = 196m2
Horses can graze in quarter circle of radius = 7m
Grazed area = 4 * (pie r2)/4 = 154 m2
Area of plot when horses cannot reach = (196 - 154) = 42m2
Ungrazed area = 42 - 20 = 22m2
Horses can graze in quarter circle of radius = 7m
Grazed area = 4 * (pie r2)/4 = 154 m2
Area of plot when horses cannot reach = (196 - 154) = 42m2
Ungrazed area = 42 - 20 = 22m2
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Four horses are tethered at four comers of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.a)42 m2b)22 m2c)84 m2d)168 m2Correct answer is option 'B'. Can you explain this answer?
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