Download Measurement 4 - Pyramid-Cone Surface Area_1

Math 10C
Measurement Lesson #4
Surface Area of Pyramids & Cones
Objective: By the end of this lesson you will be able to:
- Determine the surface area of a right pyramid and a right cone
- Define lateral area and determine when it is appropriate to only find the lateral area of a
pyramid and cone
- Solve for a missing dimension of a pyramid or cone, given the surface area
Recall: To find surface area of an object with flat faces:
Surface are is measured in _____________ units.
A right pyramid is
apex
In the diagram:
b=
h=
s=
The area of a triangle is:
To find the area of a triangular face, you must use the _______________________ as the height
of each triangular face.
e.g. 1) Find the area of the pyramid above (including the base), if b = 15”, h = 17.5”, and s = 19”.
The area of the triangular faces is also known as the ________________ ________ (denoted AL ).
Math 10C
Measurement Lesson #4
A regular tetrahedron is
e.g. 2) Find the surface area of the regular tetrahedron shown.
Sometimes the height of the pyramid is given instead of the slant height. Then we have to use the
________________________ _____________ to find the slant height.
e.g. 3) A skylight has the shape of a right pyramid. The square base measures 1.2 m by 1.2 m,
and the height is 1.6 m.
a) Draw a sketch of this pyramid.
b) Find the slant height of the pyramid to the nearest tenth.
c) Determine the area of glass that would be needed for this skylight to the nearest tenth.
(Hint: there is no glass needed for the base of the pyramid.)
Math 10C
Measurement Lesson #4
There is another formula for the surface area of a right pyramid:
Surface Area of a Right Pyramid with a Regular Polygon Base:
s
e.g. 4) A paperweight is in the shape of a hexagonal pyramid. It has a base side length of 2.8 cm
and a slant height of 7.8 cm. The area of the base is 20.4 cm2. Determine the surface area
of the paperweight using the formula above.
s
Recall: Surface area of a cylinder:
A right cone is
We can find the surface area of a right cone by using the formula for the surface area of a right
pyramid, as follows:

What is the perimeter of the base of the cone (a circle)?

What is the area of the base (a circle)?
Math 10C
Measurement Lesson #4
Therefore, the Surface Area of a Right Cone is:
e.g. 5) Determine the surface area of the cone shown to the nearest tenth.
Sometimes we are given the surface area and need to work backwards to find a missing
measurement.
e.g. 5) The lateral area of a cone is 220 cm2. The diameter of the cone is 10 cm.
a) Determine the slant height of the cone to the nearest tenth of a centimetre.
b) Determine the height of the cone to the nearest tenth of a centimetre.
Assignment:
p. 34-35 #5-12, 15-16, 18, 21
For a challenge: #13