### g_lesson_312

```Lesson 31
Surface Area and Volume of Pyramids
Homework WS 7.3
Surface Area and Volume - Pyramids
Surface Area Formula:
SA = ½lp + B
_________________________
Surface Area and Volume - Pyramids
the shape of the base
First thing to look for: _____________________________________
l
height
__________________
slant
height
__________________
(or altitude)
side
__________________
square pyramid
__________________________________
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 = 84 + 36
SA = 120
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
Surface Area and Volume - Pyramids
The __________________of
a solid is the total
volume
number of cubes that will exactly fill the interior.
Volume Formula:
V = ⅓Bh
_________________________
area of the base
Where B is:________________________
Volume – Pyramid
shape of the base
First thing to look for: _____________________________________
7.6
3. V = ⅓Bh
V = ⅓(12)(7.6)
V = 30.4 m³
3m
4m
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
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
42
4
V = ⅓(16)42
V = 30.2
4
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.
12
5
V = ⅓Bh
100= ⅓(½(5)12)h
100= ⅓(30)h
100= 10h
10 = h
Surface Area and Volume - Pyramids
7. Find the surface area of a pyramid with the given
dimensions.
shape of the base
First thing to look for: _____________________________________
n = 3, s = 14, l = 14
SA = ½lp + B
SA = ½(14)42 + ½(14)73
SA = 294 + 84.9
SA = 378.9
triangle
__________________
14
73
7
14
14
```