Solids – Volume and Area We will be using primarily 4 solid objects in this lesson. Right Circular...

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


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



4 in

10 in


Example : Find the volume and surface area of the given right circular cylinder.



4 in

10 in



hr 2 Volume

inches cubic 4.502

in 10in 1614.3

in 10in 414.32

2

V

V

V



4 in

10 in



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


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.


Right Circular Cone

6 cm

8 cm10 cm

hr 2 3

1 Volume

2 Area Surface rrs


3

2

2

cm 44.301

cm 8cm 3614.33

1

cm 8cm 614.33

1

V

V

V


Right Circular Cone

6 cm

8 cm10 cm

hr 2 3

1 Volume

2 Area Surface rrs


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


Rectangular Prism

6 ft


19 ft

7 ft

Example # 3 : Find the volume and surface area of the given rectangular prism.


Rectangular Prism

6 ft


19 ft

7 ft


feet cubic 798

ft 6ft 7ft 19

V

V


Rectangular Prism

6 ft


19 ft

7 ft


feet cubic 798

ft 6ft 7ft 19

V

V

2

222

ft 578SA

ft 84ft 266ft 228SA

ft 7ft 62ft 7ft 192ft 19ft 62SA



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.



9 m

18 m

hb2 3

1 Volume

22 Area Surface bbs

12.7 m


3

2

2

m 972

m 9m 3243

1

m 9m 183

1

V

V

V



9 m

18 m

hb2 3

1 Volume

22 Area Surface bbs

12.7 m


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



10 m 18 m




10 m 18 m


In this example, we are missing the base measurement of the pyramid.



10 m 18 m



To find the measurement of the base, we can use Pythagorean theorem :



10 m 18 m



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



10 m 18 m


Solids – Volume and Area We will be using primarily 4 solid objects in this lesson. Right Circular...

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Transcript of Solids – Volume and Area We will be using primarily 4 solid objects in this lesson. Right Circular...