Radius, Diameter, Circumference, and Area

15.1: Radius, Diameter, Circumference, and Area. Original editorial SAT preparation with three worked examples, ten flashcards, and thirty practice questions. Educator-review draft.

Lesson 1 of 63 parts Practice Flashcards

1/3

Radius and diameter

Objective: Convert a diameter to a radius.

Prerequisite skills: circle vocabulary and basic powers. Every radius joins the center to a circle point. A diameter passes through the center and contains two radii in a straight line. The radius used in circle formulas is therefore half a given diameter. Common error: substituting the full diameter into a radius formula. Restrictions and interpretation: Radius is half the diameter; circumference is a length and area is in square units.

Formulas

$d=2r$

Worked examples

Try itA circle has diameter 48. What is its radius?Show answer

Use r=d/2. Divide 48 by 2 to obtain r=24. Therefore the requested answer is 24.

Swipe sideways to move between sections

Radius and diameter

Objective: Convert a diameter to a radius.

Formulas

$d=2r$

Worked examples

Try itA circle has diameter 48. What is its radius?Show answer

Use r=d/2. Divide 48 by 2 to obtain r=24. Therefore the requested answer is 24.

Circumference

Objective: Compute boundary length from radius or diameter.

A circle circumference is 2πr or πd. If a question asks for the coefficient of π, keep π symbolic and report only its numerical multiplier. This avoids unnecessary rounding. Common error: using πr² when asked for boundary length. Restrictions and interpretation: Radius is half the diameter; circumference is a length and area is in square units.

Formulas

$C=2πr=πd$

Worked examples

Try itA circle has radius 24. Its circumference is Kπ. What is K?Show answer

Use C=2πr=2π(24)=48π, so K=48. Area would use r² instead. Therefore the requested answer is 48.

Area and inverse area

Objective: Recover a radius or diameter from a circular area.

A=πr². Divide by π to isolate r², then take the nonnegative square root. If a diameter is requested, double the radius only after finding it. Common error: reporting the radius when the question asks for the diameter. Restrictions and interpretation: Radius is half the diameter; circumference is a length and area is in square units. Desmos and method choice: Use Desmos for arithmetic or a graph/table check when that reduces work. Enter parentheses explicitly and verify the requested quantity and units. Use the algebraic steps shown here for an exact result; a rounded graph display is not proof of exact equality.

Formulas

$r=√(A/π); d=2√(A/π)$

Worked examples

Try itA circle has area 729π square units. What is its diameter?Show answer

Divide A=πr² by π: r²=729. The nonnegative root is r=27. Diameter=2r=54. Therefore the requested answer is 54.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Next lessonCentral Angles, Inscribed Angles, and Arcs