Agoat is tethered (tied up) to a stake in the ground with a 5 m rope. the goat can graze to the full length of the rope a full 360 degrees around the stake. how much area does the goat have in which to graze?

The answer to your question is  

d.

78.5 m^2

78.54 m² is your answer. So to recap, a goat tethered to a stake in the ground with a 5 m rope has 78.54 meters to graze.

We get this answer by putting the information into an equation. We know that a circle has 360° (360 degrees) and so when we see the problem say that the goat can graze 360 degrees around the stake, we instantly know it's talking about a circle. Look at the question, it's asking about the area of the circle. Now we can make an equation to find the area of this circle.

The area of a circle is A = πr²

That's Area = Pi times Radius squared.

We'll use 3.14 as substitute for Pi. The radius was given to us, it is 5 m. Put the information into the formula.

A = 3.14 * 5²

Now we do the order of operations. In the order of operations, we have no parenthesis to work with, but we do have an exponent. So we take 5 to the second power, (5² = 5 * 5) and we update our problem.

A = 3.14 * 25

Now we finish the problem by multiplying 3.14 and 25.

A = 78.54

We're not entirely done. Now we include our units of measurement. In this case, we were using m for meters. When solving for area, the unit is always squared in the final answered. So this would be our final

A = 78.54 m²