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Answer :
The equation to find the length of the rope is r² = 38.51. The correct answer is B
Let's break down the equation step by step.
The formula for the area of a circle is given by A = π * r², where A represents the area and r represents the radius of the circle.
In this scenario, the area grazed by the goat is given as 38.5 m². We want to find the length of the rope, which is represented by the radius (r) of the circular area grazed by the goat.
To set up the equation, we substitute the given area into the formula:
A = π * r²
38.5 = π * r².
This equation states that the area grazed by the goat, 38.5 m², is equal to π (pi) multiplied by the square of the radius (r) of the circular area.
Therefore, the correct equation to find the length of the rope is:
b. r² = 38.5.
This equation implies that if you square the radius of the circle (r) in meters, it will result in 38.5. The correct answer is B
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Rewritten by : Barada
The equation r² = 38.5/π relates the area (38.5 m²) to the length of the rope (L).
Let's assume the length of the rope is represented by 'L' (in meters). The goat can move in a circular area around the point where it is tied. The area grazed by the goat forms a circle with a radius equal to the length of the rope.
The formula to calculate the area of a circle is given by:
[tex]A = \pi * r^2[/tex]
where A is the area and r is the radius.
In this case, the area grazed by the goat is given as 38.5 m². We can set up the equation as follows:
[tex]38.5 = \pi * r^2[/tex]
[tex]r^2=38,5/\pi[/tex]
This equation relates the area (38.5 m²) to the length of the rope (L).
The equation r² = 38.5/π relates the area (38.5 m²) to the length of the rope (L).
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