Section1.4B Surface Area of Cones­solutions
October 03, 2016
Review From 1.4A
Things to remember
­ surface area is the area of all the sides added together
­ If the apex height is given, you must use the Pythagorean theorem to determine the slant height.
­ All triangles may not be the same!
­ Don't forget units!
Example
Determine the surface area of the following pyramid
Sep 27­7:09 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Section 1.4: Surface Areas of Right Pyramids and Cones
Sep 19­10:23 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
A right circular cone is 3-Dimensional object that has a
circular base and a curved surface.
The Surface Area of a Right Cone with slant height, s, and radius, r,
is given by the formula:
SA = lateral area + area of base
2
SA = πrs + πr
Sep 26­8:04 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Case 1: Given the slant height
Example 1: Determine the surface area of the cone to the
nearest square millimeter.
Case 2: Given Apex Height - Must find slant height
Example 2: A right cone has a base radius of 4 m and a
height of 10 m. Calculate the surface area of
this cone to the nearest square meter.
Sketch a diagram. Surface area of a
cone is given by:
SA = πrs + πr
4 m
s
10 m
2
Step 1. Find the slant height of the cone.
4 m
10 m
s
Step 2. Find the surface area.
Sep 26­9:35 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Example 3: A saltwater buoy is in the shape of a right cone.
Determine the amount of reflective paint needed
to cover the entire buoy if its diameter is 60 in.
and its height must be 3 ft. 4in. ( Note r = ½ d)
Sep 28­8:50 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Finding Missing unknowns given the surface area of a
Right Cone, Prism or Cylinder.
(Major topic—study for LA)
Case 1: Given surface area of a cone – want to find slant height
2
Example 1: The surface area of a right cone is 125 in. and
its radius is 4.7 in. What is the slant height of
the right cone?
Step 1: Sketch a diagram.
A = 125 in
2
Step 2: Use the formula for Surface Area to find the
slant height, s.
s
r = 4.7 in
Sep 26­9:08 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Case 2: Given lateral area – want to find apex height.
Example 2: The lateral area of a cone is 450cm². The
diameter of the cone is 15cm. Determine the
height of the cone to the nearest tenth of a
centimeter.
15 m
**Think of an ice cream cone!
Recall: AL = πrs and r = ½d
h
s
Step 1: Use the formula for lateral area to find the slant
height, s.
Step 2: Use Pythagorean Theorem to find the height of
the cone.
Sep 28­9:00 PM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Case 3: Given surface area – want to find apex height.
2
Example 3: A right cone has a surface area of 154 cm and a radius
of 3 cm. What is the height of the cone to the nearest cm?
Sep 24­9:02 AM
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Section1.4B Surface Area of Cones­solutions
October 03, 2016
Case 4: Find the surface height of a cylinder if you are given
the height in terms of the radius.
2
Example 4: A cylinder has a surface area of 412 cm . The
height is 3 times greater than the radius.
Approximate the height of the cylinder.
Sep 28­9:10 PM
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