Mensuration

 

 

 

Contents

 

Parts of Circle

 

Area of Circle

 

Area of Sector & Length of Arc

 

Area of Triangle 

 

Volume of Cylinder

 

Surface Area of Cylinder

 

Volume of Cones & Pyramids

 

Surface Area of Cones & Pyramids

 

Volume of Sphere

 

Surface Area of Sphere

  

Quiz

 

 

Geometry Main Page

Area & Circumference of Circle 

The Greeks discovered that the circumference of any circle is about 22/7 times longer than its diameter. They name this number pi. You often see the number written as p.

Thus circumference of a circle = pd or p2r

               the area of a circle = pr2 

Example 1

Find the area and perimeter of a circle with a radius of 21cm. (Take p = 22/7) 

Circumference = pd 
                    = 2(21) x 22/7
                    = 132cm
Area = pr2 
       = 22/7 x 21 x 21
       = 1386cm2 

 
Example 2
 
The figure shows two semicircles. Find the area of the shaded part in terms of p.
 
Area big semicircle = ½(pr2)
                           = ½ x 14 x 14 x p 
                           = 308cm2
Area small semicircle = ½ x 7 x 7 x p
                              = 77cm2
Shaded area = 308 - 77
                  = 231cm2 

Example 3
 
The figure shows a circle within a square. If the area of the square is 36cm2, find the circumference of the circle. Leave your answers in terms of p.
 
Diameter = 6cm
Circumference = pd
                    = 6p cm