1. Calculate Surface Area of Pyramids & Cones
9.3
Calculate Surface Area of Pyramids & Cones

2. Pyramids
Height: the perpendicular distance between the vertex and the base
Slant Height: the height of its lateral surface

3. Pyramids
Height: the perpendicular distance between the vertex and the base
Slant Height: the height of its lateral surface

4. (slant height)2 = (height)2 + 2 1 side
Example 1
Find the Slant Height
Find the slant height of the Rainforest Pyramid. Round your answer to the nearest whole number.
To find the slant height, use the right triangle formed by the height and half of the base.
SOLUTION
Use the Pythagorean Theorem.
(slant height)2 = (height)2 + 2 1
side
Substitute 100 for height and 200 for base side length. = 2 1
· 200
= 10, ,000
Simplify. 4

5. The slant height is about 141 feet.
Example 1
Find the Slant Height
Take the positive square root.
slant height =
20,000 ≈
Use a calculator.
ANSWER
The slant height is about 141 feet. 5

6. Surface Area of a Pyramid
SA = BA + ½ PBl
Where B = Area of base,
P = perimeter of base,
& l = slant height

7. Find the surface area of the pyramid.
Example 2
Find Surface Area of a Pyramid
Find the surface area of the pyramid.
Find the area of the base. 1.
SOLUTION
B = 6  6 = 36
Find the perimeter of the base. 2.
P = = 24
Find the slant height. 3.
Use the Pythagorean Theorem.
(slant height)2 = (height)2 + 2 1
side =
Substitute. Half of 6 is 3. =
Simplify powers. 7

8. Substitute values into the formula for surface area of a pyramid. 4.
Example 2
Find Surface Area of a Pyramid
= 25
Simplify.
slant height = = 5 25
Take positive square root.
Substitute values into the formula for surface area of a pyramid. 4. 2 1
S = BA + PAl
Write the formula for surface area.
= 36 + 2 1
(24) (5)
Substitute.
Simplify.
= 96
ANSWER
The surface area of the pyramid is 96 square feet. 8

9. Find the surface area of the pyramid.
Checkpoint
Find Surface Area of a Pyramid
Find the surface area of the pyramid. 2. 1. 3.

10. Find the surface area of the pyramid.
Checkpoint
Find Surface Area of a Pyramid
Find the surface area of the pyramid. 1.
ANSWER
7*7 + ½ (28)*9=175 in.2 2.
ANSWER
35.1+ ½ (27)*12 = about cm2

11. Find the surface area of the pyramid.
Checkpoint
Find Surface Area of a Pyramid
Find the surface area of the pyramid.
ANSWER
360 ft2 3.
Find slant height
C2 = a2 + b2
C2 = (½ (10))2
C2 =
C2 =
C2 = 169
C= 13
SA = B + ½ Pl
= ½ 40*13 =

12. Where B = area of base and l = slant height
Surface Area of a Cone
SA = BA + πrl
SA = πr2 + πrl
Where B = area of base and l = slant height

13. Find the surface area of the cone to the nearest whole number.
Example 3
Find Surface Area of a Cone
Find the surface area of the cone to the nearest whole number. a.
The radius of the base is 4 inches and the slant height is 6 inches. a.
SOLUTION
Write the formula for surface area of a cone.
S = πr2 + πrl
= π(4)2 + π(4)(6)
Substitute 4 for r and 6 for l.
= 40π
Simplify 16π + 24π.
≈ 126
Multiply.
The surface area is about 126 square inches.
ANSWER 13

14. First find the slant height. b.
Example 3
Find Surface Area of a Cone
First find the slant height. b.
(slant height)2 = r2 + h2
Use the Pythagorean Theorem.
= (12)2 + (5)2
Substitute 12 for r and 5 for h.
= 169
Simplify
Find the positive square root.
slant height =
169
= 13
Simplify. 14

15. Next substitute 12 for r and 13 for l in the formula for surface area.
Example 3
Find Surface Area of a Cone
Next substitute 12 for r and 13 for l in the formula for
surface area.
Write the formula for surface area.
S = πr2 + πrl
= π(12)2 + π(12)(13)
Substitute.
= 300π
Simplify 144π + 156π.
≈ 942
Multiply.
The surface area is about 942 square feet.
ANSWER 15

16. Find the surface area to the nearest whole number.
Checkpoint
Find Surface Area of Cones
Find the surface area to the nearest whole number. 4. 5. 6.

17. Find the surface area of the cone to the nearest whole number.
Checkpoint
Find Surface Area of Cones
Find the surface area of the cone to the nearest whole number. 4.
ANSWER
691 in.2 5.
ANSWER
151 ft2 6.
ANSWER
75 cm2

19. Review: Find the surface area of the prism. 1. 72 in.2 ANSWER 2.

20. Find the surface area of the cylinder
Find the surface area of the cylinder. Round your answer to the nearest whole number. 3.
748 cm2
ANSWER 4.
170 ft2
ANSWER

21. Worksheet 9.3A
Quiz tomorrow