• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
Geometry Help
  • About
  • Privacy Policy
  • Contact Me
  • Terms of Service
  • Accessibility Statement
menu icon
go to homepage
search icon
Homepage link
  • About
  • Privacy Policy
  • Contact Me
  • Terms of Service
  • Accessibility Statement
×
Home » Area of Geometric Shapes » Circles: Finding the Area of a Ring

Circles: Finding the Area of a Ring

Last updated: Mar 27, 2021 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

In today's lesson, we will learn how to find the area of a ring. A ring is a geometric shape made up of two circles with the same center point. We call such circles "concentric". Another name for a ring is an Annulus.

Problem

A circular hot tub with radius 6 feet has a sitting area around its perimeter, with a width of 1 foot. Find the area of the sitting area.

Area of ring in geometry

Strategy

A circle is completely defined by its radius, and its area is given by  A circle =π*r2. The tub and the sitting area form two concentric circles.

We know the radius of the outer circle (the tub) - so we can find its area. We know the width of the sitting area, from which we can calculate the inner radius (from the center of the tub to the inner edge of the sitting area), and find the area of the inner circle.

If we subtract the inner area form the outer area, we get the area of the ring, which is the sitting area.

Solution

(1) Rtub= 6
(2) Aouter =π*R2=π*62=36π
(3) rinner= 6-1=5
(4) Ainner =π*r2=π*52=25π
(5) Aring =Aouter-Ainner=36π-25π=11π≈34.56

Form that last line in the solution, we can see that more generally, the area of the ring is the difference between the areas of the two circles, or Aring =Aouter-Ainner. But we can express the difference between these two areas in a compact form as Aouter-Ainner=π(R2outer-r2inner)

« Trapezoids: Adjacent angles are Supplementary
Arc Length Formula »

About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected]

Primary Sidebar

About

Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

Geometry Topics

  • Area of Geometric Shapes
  • Circles
    • Arcs, Angles, and Sectors
    • Chords
    • Inscribed Shapes
    • Tangent Lines
  • Lines and Angles
    • Intersecting Lines and Angles
    • Parallel Lines
    • Perpendicular lines
  • Pentagons and Hexagons
  • Perimeter of Geometric Shapes
  • Polygons
  • Quadrangles
    • Kites (Deltoids)
    • Parallelograms
    • Rectangles
    • Rhombus
    • Squares
    • Trapezoids
  • Triangles
    • Congruent Triangles
    • Equilateral Triangles
    • Isosceles Triangles
    • Pythagorean Theorem
    • Right Triangles
    • Similar Triangles
    • Triangle Inequalities

By accessing or using this website, you agree to abide by the Terms of Service and Privacy Policy.


Copyright © 2023