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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?
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Area of a circle= πr^2
r= d/2= 7 cm/2= 3.5 cm
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π(3.5 cm)^2= 12.25π cm^2
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Area of a triangle= (b x h)/2
b= circumference= 2πr= 7π cm h= slant height= 9 cm
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(7π cm x 9 cm)/2= 63π cm^2/2= 31.5πcm^2
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1(base)+1(lateral face)
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31.5πcm^2 + 12.25πcm^2= 43.75πcm^2
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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.
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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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