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

Surface Area of Cones & Pyramids 

Activity to find Lateral Surface Area of Cone

1. Refer to the figure shown on the right. Suppose the cone is slit along its slant height, l, a sector is formed

2. Using the following ratio, find the area of the major sector ACA', which is actually the lateral surface area of the cone.

Arc Length ACA'  =   q   

2pr  =  q   

Example 1

 

A right pyramid 12cm high stands on a square base of sides 10cm. Calculate the total surface area.

 

Total surface area = 4(½ x 13 x 10) + 10 x 10 

   

Example 2

 

A right circular cone is formed by bending a semicircular piece of paper of radius 8cm. Determine the slant height l and the curved surface area of the cone, corrected to 1 decimal place.

 

l = 8cm

 

Curved surface area = ½ x 8 x 8 x p

                            = 100.5cm² (1 d.p.)

Example 3

 

Two canvas tents are made differently. One has a rectangle base 2m by 1.4m and height 2m. The other tent is in the shape of a cone of radius 1m and height 2m. Which tent requires more canvas to make, and by how much?

 

Slant height of width

Slant height of length

Surface area of pyramid = 2(½ x x 1.4) + 2(½ x x 2) 

                                  = 7.368cm² 

Slant height of cone

Surface area of cone = p x 1 x

                             = 7.025cm² 

Difference in area = 7.368cm² - 7.025cm² 

                         = 0.343cm² 

 

The pyramid tent requires more canvas to make. It needs 0.343cm² more canvas.