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Information about three circles is listed below.Circle P has a radius of 26 cm.Circle Q has a diameter of 52 cm.Circle R has a radius of 52 cm. Based on the information, which statement is true?  A.  The area of Circle Q is larger than the area of Circle R.  B.  The area of Circle P is the smallest of all three circles.  C.  The circumference of Circle Q is the same as Circle R.  D.  The circumference of Circle Q is the same as Circle P.

Question

Information about three circles is listed below.Circle P has a radius of 26 cm.Circle Q has a diameter of 52 cm.Circle R has a radius of 52 cm. Based on the information, which statement is true?  A.  The area of Circle Q is larger than the area of Circle R.  B.  The area of Circle P is the smallest of all three circles.  C.  The circumference of Circle Q is the same as Circle R.  D.  The circumference of Circle Q is the same as Circle P.

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Solution

The correct answer is D. The circumference of Circle Q is the same as Circle P.

Here's why:

The formula for the circumference of a circle is 2πr (where r is the radius).

For Circle P, the radius is given as 26 cm. So, the circumference is 2π * 26 = 52π cm.

For Circle Q, the diameter is given as 52 cm. The radius (which is half the diameter) is therefore 26 cm. So, the circumference is 2π * 26 = 52π cm.

For Circle R, the radius is given as 52 cm. So, the circumference is 2π * 52 = 104π cm.

So, the circumference of Circle Q is the same as Circle P (both are 52π cm), and both are smaller than the circumference of Circle R (which is 104π cm). Therefore, option D is correct.

This problem has been solved

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