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Solids – Volume and Area
We will be using primarily 4 solid objects in this lesson.
Right Circular Cylinder
Right Circular Cone
r
h
hr 2 Volume 222 Area Surface rrh
r
hs
hr 2 3
1 Volume
2 Area Surface rrs
Solids – Volume and Area
We will be using primarily 4 solid objects in this lesson.
Rectangular Prism
Regular Square Pyramid
h
lwh Volume hwlwhl 222 Area Surface
h
b
hb2 3
1 Volume
22 Area Surface bbs
lw
s
Solids – Volume and Area
Right Circular Cylinder
4 in
10 in
hr 2 Volume 222 Area Surface rrh
Example : Find the volume and surface area of the given right circular cylinder.
Solids – Volume and Area
Right Circular Cylinder
4 in
10 in
hr 2 Volume 222 Area Surface rrh
Example : Find the volume and surface area of the given right circular cylinder.
hr 2 Volume
inches cubic 4.502
in 10in 1614.3
in 10in 414.32
2
V
V
V
Solids – Volume and Area
Right Circular Cylinder
4 in
10 in
hr 2 Volume 222 Area Surface rrh
Example : Find the volume and surface area of the given right circular cylinder.
hr 2 Volume
inches cubic 4.502
in 10in 1614.3
in 10in 414.32
2
V
V
V
222 A S rrh
in sq 351.8SA
in sq 100.48 in sq 2.251SA
in 414.32in 10in 414.32SA 2
Solids – Volume and Area
Right Circular Cone
6 cm
8 cm10 cm
hr 2 3
1 Volume
2 Area Surface rrs
Example # 2 : Find the volume and surface area of the given right circular cone.
Solids – Volume and Area
Right Circular Cone
6 cm
8 cm10 cm
hr 2 3
1 Volume
2 Area Surface rrs
Example # 2 : Find the volume and surface area of the given right circular cone.
3
2
2
cm 44.301
cm 8cm 3614.33
1
cm 8cm 614.33
1
V
V
V
Solids – Volume and Area
Right Circular Cone
6 cm
8 cm10 cm
hr 2 3
1 Volume
2 Area Surface rrs
Example # 2 : Find the volume and surface area of the given right circular cone.
2
22
2
cm 301.44SA
cm 04.113cm 4.188SA
cm 614.3cm 10cm 63.14SA
3
2
2
cm 44.301
cm 8cm 3614.33
1
cm 8cm 614.33
1
V
V
V
Solids – Volume and Area
Rectangular Prism
6 ft
lwh Volume hwlwhl 222 Area Surface
19 ft
7 ft
Example # 3 : Find the volume and surface area of the given rectangular prism.
Solids – Volume and Area
Rectangular Prism
6 ft
lwh Volume hwlwhl 222 Area Surface
19 ft
7 ft
Example # 3 : Find the volume and surface area of the given rectangular prism.
feet cubic 798
ft 6ft 7ft 19
V
V
Solids – Volume and Area
Rectangular Prism
6 ft
lwh Volume hwlwhl 222 Area Surface
19 ft
7 ft
Example # 3 : Find the volume and surface area of the given rectangular prism.
feet cubic 798
ft 6ft 7ft 19
V
V
2
222
ft 578SA
ft 84ft 266ft 228SA
ft 7ft 62ft 7ft 192ft 19ft 62SA
Solids – Volume and Area
Regular Square Pyramid
9 m
18 m
hb2 3
1 Volume
22 Area Surface bbs
12.7 m
Example # 4 : Find the volume and surface area of the given regular square pyramid.
Solids – Volume and Area
Regular Square Pyramid
9 m
18 m
hb2 3
1 Volume
22 Area Surface bbs
12.7 m
Example # 4 : Find the volume and surface area of the given regular square pyramid.
3
2
2
m 972
m 9m 3243
1
m 9m 183
1
V
V
V
Solids – Volume and Area
Regular Square Pyramid
9 m
18 m
hb2 3
1 Volume
22 Area Surface bbs
12.7 m
Example # 4 : Find the volume and surface area of the given regular square pyramid.
3
2
2
m 972
m 9m 3243
1
m 9m 183
1
V
V
V
2
22
2
m 2.781SA
m 324m 2.457SA
m 18m 7.12m 182SA
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
10 m 18 m
The base will be two times
larger than the missing leg…
x
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
10 m 18 m
The base will be two times
larger than the missing leg…
x
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
10 m 18 m
The base will be two times
larger than the missing leg…
x
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
10 m 18 m
The base will be two times
larger than the missing leg…
x
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
10 m 18 m
The base will be two times
larger than the missing leg…
x
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
In this example, we are missing the base measurement of the pyramid.
To find the measurement of the base, we can use Pythagorean theorem :
10 m 18 m
The base will be two times
larger than the missing leg…
x
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.
Solids – Volume and Area
Regular Square Pyramid
10 m 18 m
Example # 5 : Find the volume and surface area of the given regular square pyramid.