A goat is tied by a rope 2.5m long to a peg in some grass. The goat eats 1sqm of grass in 28 minutes. How long does it take to eat all that it can reach?
the area of a circle is πr^2
So, to convert that to time,
6.25π m^2 * 28min/1m^2 = 549.778 min
assuming that the entire circle is covered by grass.
Well, it seems like our goat friend is quite eager to feast on that grass! Now, let me calculate this in a rather unorthodox but amusing way.
First things first, let's imagine the goat has a superpower - let's call it "Grass-Munching-a-Tron 3000." With this superpower, our goat can eat an entire square meter of grass in just 28 minutes. Impressive, right?
Now, let's calculate the area that the goat can reach. If we consider the goat as the center point and the rope as the radius, we get a circle with an area of π * r². So, the goat can graze on an area equal to π * (2.5m)².
Now, with our Grass-Munching-a-Tron 3000 in action, the goat can devour 1 square meter of grass in 28 minutes. But how many square meters are there in π * (2.5m)²?
Let's do a quick calculation: π * (2.5m)² ≈ 19.635 square meters.
Now, if the goat can feast on 1 square meter in 28 minutes, it would need 19.635 times longer to eat its entire reachable area. Therefore, the goat would need approximately 548.58 minutes to eat all the grass it can reach.
So, my grass-loving friend, the goat would need around 548.58 minutes to munch on all the grass within its reach. Now, that's what I call a grass-gobbling marathon!
To calculate the amount of grass that the goat can reach, we need to find the area of the circle formed by the rope. The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.
Given that the length of the rope is 2.5m, the radius (r) is half of that, which is 2.5m/2 = 1.25m.
Now, we can calculate the area of the circle: A = π(1.25m)^2.
Let's calculate this:
A = π(1.25m)^2
A = π(1.5625m^2)
A = 4.9m^2 (approx.)
Since the goat eats 1 square meter of grass in 28 minutes, it can eat 4.9 square meters of grass in 28 minutes.
To calculate how long it takes to eat all the grass it can reach, we divide the total grass area by the eating rate:
Time = Total grass area / Eating rate
Time = 4.9m^2 / 1m^2 per 28 minutes
Now, let's calculate this:
Time = 4.9m^2 / 1m^2 per 28 minutes
Time = 4.9 * 28 minutes
Time = 137.2 minutes (approx.)
Therefore, it will take approximately 137.2 minutes for the goat to eat all the grass it can reach.
To determine how long it takes for the goat to eat all the grass it can reach, we need to calculate the area that is accessible to the goat within the length of the rope.
The goat can move around within a circle with a radius equal to the length of the rope (2.5m). The area of a circle is given by the formula A = πr^2, where A represents the area and r represents the radius.
Plugging in the values, we have:
A = π(2.5)^2
A ≈ 3.14 * 2.5^2
A ≈ 19.625 square meters
Therefore, the goat can access approximately 19.625 square meters of grass.
Since the goat eats 1 square meter of grass in 28 minutes, we can calculate the time it takes to eat 19.625 square meters. We divide the total area by the rate of eating:
Time = Total Area / Rate of Eating
Time = 19.625 square meters / 1 square meter per 28 minutes
Time ≈ 19.625 * 28
Time ≈ 549.5 minutes
Therefore, it takes approximately 549.5 minutes for the goat to eat all the grass it can reach.