Homework Solutions
Geometry CP, Apr 15
Surface Areas of Pyramids, Cones, and Spheres
Book Section: 12-3, 12-6
Essential Question: How can I compute the surface areas of pyramids,
cones, and spheres?
Standards: G-1.9; CCSS G.GMD.1, .3; G-7.6, .1, .5
Evaluating Formulas
•
“Plug-and-chug” mathematics
•
After you have chosen or know what formula to use:
 List all required arguments
 Substitute known values for variables (Look at or draw a
picture)
 Solve for desired or unknown quantities (Pythagorean Theorem,
trigonometry)
 Work it out step-by-step
 Use units when required
Definitions
• Regular Pyramid – A pyramid whose base is a
regular polygon. All lateral faces are congruent
triangles.
• Height (h) – The distance from the vertex to the
base, perpendicular to the base.
• Slant height (l) – The distance from the vertex
to the base along a lateral face. This distance is
the height of the triangular lateral face.
Picture This
height
Regular Pyramid Lateral Area
Example 1
Lateral Area of a Regular Pyramid
Find the lateral area of
the square pyramid.
Example 2
Find the lateral area of the square pyramid.
A. 54 in2
B. 64 in2
C. 108 in2
D. 132 in2
Regular Pyramid Surface Area
Example 3
Surface Area of a Square Pyramid
Find the surface area of the square pyramid to the
nearest tenth.
Example 4
Find the surface area of the square
pyramid to the nearest tenth.
A. 96 in2
B. 124.3 in2
C. 138.5 in2
D. 156 in2
Cones
l is the cone slant height
• Cone
• Net of Cone
Cone Lateral and Surface Area
Example 5
Lateral Area of a Cone
ICE CREAM A sugar cone has an altitude of
8 inches and a diameter of 2.5 inches. Find the lateral
area of the sugar cone.
Example 6
Surface Area of a Cone
Find the surface area of the
cone. Round to the nearest
tenth.
Example 7
Find the surface area of the cone. Round to the nearest
tenth.
A. 58.2 cm2
B. 61.3 cm2
C. 63.6 cm2
D. 70.7 cm2
Sphere Surface Area
Example 8
Surface Area of a Sphere
Find the surface area of the
sphere. Round to the nearest
tenth.
Example 9
Find the surface area of the sphere. Round to the nearest
tenth.
A. 462.7 in2
B. 473.1 in2
C. 482.6 in2
D. 490.9 in2
Definition
• Great Circle of a hemisphere – A half sphere
(or hemisphere) has a bottom that is a circle of
the same diameter as the sphere.
• When finding the surface area of a hemisphere,
calculate the surface area of the sphere, divide it
by 2 and then add the area of the great circle.
Hemisphere S = 2πr2 + πr2 = 3πr2
Example 10
Use Great Circles to Find Surface Area
A. Find the surface area of the hemisphere.
Concept Summary
Examples
Classwork: Textbook p.859, 6, 8; p.884,
12, 20
Homework: HW Due 4/19, 1-6