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There is a vast grassy farm in which there is a rectangular building of the farmhouse whose length and breadth is 50m and 40m respectively. A horse is tethered at a corner of the house with a tether of 80m long. What is the maximum area that the horse can graze?
- a)5425π
- b)5245π
- c)254π
- d)None of These
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
There is a vast grassy farm in which there is a rectangular building ...
The maximum area that the horse can graze can be determined by drawing a circle with a radius of 80m around the corner where the horse is tethered.
To find the maximum area, we need to determine the area of the circle. The formula for the area of a circle is given by A = πr^2, where A is the area and r is the radius.
In this case, the radius is given as 80m, so we can substitute this value into the formula to find the area.
A = π(80)^2
A = 6400π
Therefore, the maximum area that the horse can graze is 6400π square meters.
However, we need to consider the fact that the rectangular building of the farmhouse is in the way and restricts the grazing area.
To calculate the area that the horse cannot graze, we need to subtract the area of the rectangular building from the maximum area of the circle.
The area of the rectangular building is given by A = length × breadth, which is 50m × 40m = 2000 square meters.
Subtracting this from the maximum area of the circle, we get:
6400π - 2000 = 4400π square meters.
Therefore, the maximum area that the horse can graze is 4400π square meters.
However, none of the answer options match this value. The closest option is option A, which is 5425π square meters. This is a slightly larger area than the actual maximum grazing area.
Therefore, the correct answer is none of these (d) as none of the given options match the calculated grazing area.
To find the maximum area, we need to determine the area of the circle. The formula for the area of a circle is given by A = πr^2, where A is the area and r is the radius.
In this case, the radius is given as 80m, so we can substitute this value into the formula to find the area.
A = π(80)^2
A = 6400π
Therefore, the maximum area that the horse can graze is 6400π square meters.
However, we need to consider the fact that the rectangular building of the farmhouse is in the way and restricts the grazing area.
To calculate the area that the horse cannot graze, we need to subtract the area of the rectangular building from the maximum area of the circle.
The area of the rectangular building is given by A = length × breadth, which is 50m × 40m = 2000 square meters.
Subtracting this from the maximum area of the circle, we get:
6400π - 2000 = 4400π square meters.
Therefore, the maximum area that the horse can graze is 4400π square meters.
However, none of the answer options match this value. The closest option is option A, which is 5425π square meters. This is a slightly larger area than the actual maximum grazing area.
Therefore, the correct answer is none of these (d) as none of the given options match the calculated grazing area.
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Community Answer
There is a vast grassy farm in which there is a rectangular building ...
The length of tether of the horse is 80m.
Area grazed by horse
= 
= 
= 5425πm2
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