MPM1D
Surface Area of Pyramids and Cones
Unit 6 Lesson 6
When the new entrance to the Louvre was built in Paris, architects and builders needed to know how
much glass was needed to construct the triangular surfaces of the two square-based pyramids. When a
company manufactures a paper cup, the amount of material required must be known. To calculate
these amounts, formulas for the surface area of pyramids and cones are required.
The surface area of a square-based prism consists of one square and four identical triangles.
SA 1 square
4 triangles
=
SA
b2
2bs
NOTE: Since we are measuring the area of the triangles found on the SURFACE of the figure, it is
the external slant height (s) that must be used.
If the vertical height (h) is given, the Pythagorean theorem must be used to calculate the slant
height (s).
Find the surface area of the following pyramids.
1)
2)
MPM1D
Surface Area of Pyramids and Cones
page 2
The surface area of a cone consists of a circle plus a curved side, the lateral surface, which when
flattened is a sector of a circle.
SA 1 circle 1 curved side
SA
r2
rs
Again slant height (s) is used for surface area calculations.
TRY THESE:
3)
A cone has a radius of 5 cm and a slant height of 12 cm. Calculate its surface area.
Watch out for questions involving PARTIAL surface area.
4)
A conical paper cup is 10 cm deep and has a diameter of 8 cm.
a) How much paper is needed to make the cup?
b) How much liquid can it hold?
Text page 439 #4c, 5, 7, 9, 10, 12 and page 454 #13-14