Question

The circle and rectangle, with radius and side lengths shown, have the same area. Knowing this, which is a possible way to find the area of a circle?

A. Multiply the circumference by the diameter.


B. Multiply the circumference by half the radius.


C. Multiply twice the circumference by the diameter.


D. Multiply twice the circumference by half the radius.

Answer 1

The circle and the rectangle have the same area and we have the lenght and widht of rectangle, so we can discover rectangle area and it will be the same as circle.

A = 2πr . r/2

A = πr²

The answer will be B, because the circumference is 2πr and half a radius is r/2

And as shown: 2πr . r/2 = πr²

Answer 2

B

Explanation:

The point to this question is that the rectangle and the circle have the same area.

The circumference of a circle is 2*pi*r. You want to wind up with pi r^2

Area = (2 * pi * r) * (r/2) is what the rectangle tells you to do.

Area = Circumference * r/2 which is B. No other answer will give you this result.

Answer

• A: Circumference * diameter = 2*pi*r * 2r = 4pi r^2 Too Big. Answer not A.
• B: Answer
• C: 2(2*pi*r) * (2*r) = 8 pi r^2 this is likely your worst answer.
• D: 2(2*pi*r) * r/2 = 2*pi*r^2 which is twice the area.