1. Lesson 31
Surface Area and Volume of Pyramids
Homework WS 7.3

2. SA = ½lp + B Surface Area and Volume - Pyramids Surface Area Formula:
_________________________
SA = ½lp + B

3. the shape of the base l slant height height side square pyramid
Surface Area and Volume - Pyramids
the shape of the base
First thing to look for: _____________________________________ l
slant height
height
__________________
__________________
(or altitude)
side
__________________
square pyramid
__________________________________

4. Square-lw SA = ½lp + B SA = ½lp + lw SA = ½(7)(24) + 36 SA = 84 + 36
Surface Area – Pyramid
1. Find the surface area of each regular pyramid with side length s, and slant height l. The number of sides of the base is given by n.
s = 6 l = 7 n = 4
Square-lw
SA = ½lp + B
SA = ½lp + lw
SA = ½(7)(24) + 36
SA =
SA = 120

5. shape of the base triangle SA = ½lp + B SA = ½lp + ½bh
Surface Area and Volume - Pyramids
2. Find the surface area with side length s and slant height l, with the number of sides of the base given by n.
shape of the base
First thing to look for?: _____________________________________
s =8 L = 9 n = 3
triangle
__________________
SA = ½lp + B
SA = ½lp + ½bh
SA = ½(9)(24) + ½(8)(43)
SA = 135.7

6. volume V = ⅓Bh area of the base Surface Area and Volume - Pyramids
The __________________of a solid is the total number of cubes that will exactly fill the interior.
Volume Formula:
_________________________
V = ⅓Bh
area of the base
Where B is:________________________

7. shape of the base 3. V = ⅓Bh V = ⅓(12)(7.6) V = 30.4 m³
Volume – Pyramid
shape of the base
First thing to look for: _____________________________________
3. V = ⅓Bh
7.6
V = ⅓(12)(7.6)
V = 30.4 m³ 3m 4m

8. Surface Area and Volume - Pyramids
4. A pentagonal pyramid with a base area of 24 square units and a volume of 104 cubic units. What is the height?
V = ⅓Bh
104 = ⅓(24)h
104 = 8h
13 = h

9. Surface Area and Volume - Pyramid
5. Find the volume of a square pyramid with the given dimensions.
Base edge of 4, and a height equal to the diagonal of the base
V = ⅓Bh
V = ⅓(16)42
42 4
V = 30.2 4

10. V = ⅓Bh 100= ⅓(½(5)12)h 100= ⅓(30)h 100= 10h 10 = h
Surface Area and Volume - Pyramid
6. A pyramid has a right triangle as its base, with leg lengths of 5 and 12. If the pyramids volume is 100, find its altitude.
V = ⅓Bh
100= ⅓(½(5)12)h
100= ⅓(30)h 12
100= 10h
10 = h 5

11. shape of the base triangle SA = ½lp + B SA = ½(14)42 + ½(14)73 14 14
Surface Area and Volume - Pyramids
7. Find the surface area of a pyramid with the given dimensions.
n = 3, s = 14, l = 14
shape of the base
First thing to look for: _____________________________________
triangle
__________________
SA = ½lp + B
SA = ½(14)42 + ½(14)73 14 14
73
SA = 7
SA = 378.9 14