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Circumference, Area,
Surface Area, and Volume
By Taylor Winter
Derive the Formula:
Surface area of a Cone
Example Problems
1. A cone has a diameter of 7 cm and a slant height of 9 cm. What is the surface area of the cone?
Area of a circle= πr^2
r= d/2= 7 cm/2= 3.5 cm
π(3.5 cm)^2= 12.25π cm^2
Area of a triangle= (b x h)/2
b= circumference= 2πr= 7π cm h= slant height= 9 cm
(7π cm x 9 cm)/2= 63π cm^2/2= 31.5πcm^2
1(base)+1(lateral face)
31.5πcm^2 + 12.25πcm^2= 43.75πcm^2
The surface area of the cone is 43.75πcm^2.
Similar to the prism surface area you should draw the net of the pyramid. After that you find the area of the shapes and add them together.
The only difference is that in cones there is slant height, or the height of the 'triangle', which is separate from the height of the cone.
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