Suppose the two "legs" of the compass shown in the illustration are adjusted so that the distance between the pointed ends is 3 inches. What will the area of the circle be, if ?
A) 28.26
B) 18.84
C) 3.1415926536
D) 6
E) none of these

Question

Suppose the two "legs" of the compass shown in the illustration are adjusted so that the distance between the pointed ends is 3 inches. What will the area of the circle be, if  ? 
A) 28.26 
B) 18.84 
C) 3.1415926536 
D) 6 
E) none of these

Quizplus · Accepted Answer

First, we can use the formula for the area of a circle:

A = πr^2

Next, we need to find the radius of the circle. We can do this by finding the midpoint of the line segment between the pointed ends of the compass, which will be the center of the circle.

Since the distance between the pointed ends of the compass is 3 inches, the midpoint will be 1.5 inches away from each end.

We can use the Pythagorean theorem to find the distance from the midpoint to one of the pointed ends:

a^2 + b^2 = c^2

(1.5)^2 + (3/2)^2 = r^2

r ≈ 1.837 inches

Now we can plug this value into the formula for the area of a circle:

A = π(1.837)^2

A ≈ 28.26

Therefore, the answer is A) 28.26.

Suppose the Two "Legs" of the Compass Shown in the Illustration