FCP 10
1.4 Surface Area of Right Pyramids and Right Cones
In previous grades you have worked with surface area when dealing with rectangular
prisms and cylinders.
Surface Area is:
When looking at surface area, it is sometimes best if you can break the 3 dimensional
shapes into all of the individual shapes that compose it. There are times as well where
you can simply use a formula, provided you are given the right information.
When using any formulae it is important to use ____________ when substituting
numerical values into it.
Quick Review:
Find the Surface Area of:
Find the Surface Area of:
Formula:
Cones and Right Pyramids:
Cones and right pyramids can be tricky as they contain both a _____ and a _____height
Do you think the slant height is smaller or larger than the actual height?
The formula sheet that you are given contains a lot of information. It contains formulas
for surface area and volume. It also breaks up different shapes into areas of sides and
areas of the base. Together these usually form the surface area of the entire shape.
It is important in this unit to first identify ________________________, and choose
a formula that will get you to the answer, and then find all elements of the formula so
you can use it.
Example 1:
Find the surface Area of the following cone
Example 2:
A right cone has a base radius of 2 ft. and a height of 7 ft. Calculate the surface area
of this cone to the nearest square foot.
Example 3:
2
The lateral area of a cone is 220 cm . The diameter of the cone is 10cm. Determine the
height of the cone to the nearest tenth of a centimetre.
Lateral Area:
This is a question where we are given an Area, and we have to solve for a part of the
formula‼!
Right Pyramids:
Right pyramids can be very tricky as you will usually have to find the area of the
triangles that form the sides, as well as the square or rectangular base.
The height of the triangles is actually the _________ height of the 3D shape they
came from
Example 4:
A right rectangular pyramid has base dimensions 8 ft. by 10 ft., and a height of 16ft.
Calculate the surface area of the pyramid to the nearest square foot.
Example 5:
Jeanne-Marie measured then recorded the lengths of the edges and slant height of this
regular tetrahedron. What is its surface area to the nearest square centimetre?