12.3 Surface Areas of Pyramids and Cones
Name_______________________________
Learning Objective: After this lesson, you should be able to successfully find the lateral area and surface area
of pyramids and cones.
Standard: G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and
identify three-dimensional objects generated by rotations of two-dimensional objects.
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a
circle, volume of a cylinder, pyramid, and cone.
G.MG.2 Apply concepts of density based on area and volume in modeling situations
Exercises - Find the lateral area and surface area of each regular pyramid. Round to the nearest tenth if
necessary.
A)
B)
 = ________
 = ________
P = _____________
P = _____________
LA = _____________
LA = _____________
B = _____________
B = _____________
SA = _____________
SA = _____________
12.3 More Practice on Surface Areas of Pyramids and Cones
Find the lateral area and surface area of each regular pyramid. Round to the nearest tenth if necessary.
1.
2.
 = ________
 = ________
P = _____________
P = _____________
LA = _____________
LA = _____________
B = _____________
B = _____________
SA = _____________
SA = _____________
Find the lateral area and surface area of each cone. Round to the nearest tenth if necessary.
3.
=
4.
_________
=
_________
LA = ____________
LA = ____________
Area of base = ________
Area of base = ________
SA = ____________
SA = ____________
5. Find the surface area of a cone if the height is 14 centimeters and the slant height is 16.4 centimeters.
6. Find the surface area of a cone if the height is 12 inches and the diameter is 27 inches.
7. HATS Chad bought a conical hat on a recent trip to central Vietnam. The basic frame of the hat is 16 hoops of
bamboo that gradually diminish in size. The hat is covered in palm leaves. If the hat has a diameter of 50
centimeters and a slant height of 32 centimeters, what is the lateral area of the conical hat?
Find the Lateral Area and Surface Area. Round to the nearest tenth if necessary.
8.
9.
10.
L. A. = __________
L. A. = ______________
L. A. = ___________
S. A. = __________
S. A. = ______________
S. A. = ___________
11.
12.
13.
.
L. A. = __________
L. A. = ___________
L. A. = __________
S. A. = __________
S. A. = ____________
S. A. = __________
14.
15.
16.
L. A. = _________
L. A. = _________
L. A. = _________
S. A. = _________
S. A. = _________
S. A. = _________
Answers: 1. 10 yd, 36 yd, 180 yd2, 81 yd2, 261 yd2 3. 6.4 m, 80.4 m2, 50.2 m2, 130.6 m2
7. 2512 cm2 9. 489.9 in2, 942.0 in2 11. 260 cm2, 360 cm2 13. 289.7 m2, 353.3 m2
15. 7215 m2, 11440 m2
5. 664.6 cm2