1. Trenton Public Schools
Area and Volume
Slide Presentation By
Mr. Michael Braverman
Trenton Public Schools
March 2015

2. Area and Volume Definitions 1 foot Area:
1 ft2
Definitions
Area:
The number of UNIT SQUARES it takes to completely cover an object without gaps or overlap.
Area is ALWAYS given in SQUARE units (or units2)
All area FORMULAS are based on the formula of a rectangle (Area = base x height) – see AREA slide show for more.

3. Area and Volume 3 feet 15 feet2 5 feet
All area FORMULAS are based on the formula of a rectangle (Area = base x height)
3 feet
15 feet2
1 foot
1 ft2
5 feet

4. Area and Volume Definitions 3 Units 3 Units 5 Units Volume:
The number of unit CUBES it takes
to completely FILL an object.
3 Units
3 Units
5 Units

5. Area and Volume Definitions Volume:
1 unit
Definitions
Volume:
The number of unit CUBES it takes to completely FILL an object.
is ALWAYS given in CUBIC units (which are either units of volume or units3)

6. V=Area of the base * height of the solid.
Area and Volume
Definitions
Volume:
The number of unit CUBES it takes to completely FILL an object.
Volume is ALWAYS given in CUBIC units (which are either units of volume or units3)
All volume FORMULAS where there are two parallel and congruent bases are:
V=Area of the base * height of the solid.
V=Abase * height

7. 15 ft2 Area and Volume 5 feet 3 feet V = Abase * height 1 foot 1 foot

8. 15 ft3 Area and Volume 5 feet 3 feet V = Abase * height
The Volume of one “unit-slice” (a one-unit thick slice parallel to the base) is equivalent to the area in number, but has cubic units.
V = Abase * height
5 feet
15 ft3
3 feet
1 foot
1 foot
1 foot
1 ft3
1 foot

9. 15 ft3 Area and Volume 5 feet 3 feet V = Abase * height
All area FORMULAS are based on the formula of a rectangle (Area = base x height)
V = Abase * height
5 feet
3 feet
15 ft3
1 foot
1 foot
1 foot
1 ft3
1 foot

10. 15 ft3 Area and Volume 5 feet 3 feet V = Abase * height
1 foot
V = Abase * height
= 15 ft2 x 1 ft
= 15 ft3
1 foot
1 foot
1 ft3
1 foot

11. 15 ft3 15 ft3 Area and Volume 5 feet 3 feet V = Abase * height
1 foot
V = Abase * height
= 15 ft2 x 2 ft
= 30 ft3
V = Abase * height
= 15 ft2 x 1 ft
= 15 ft3
15 ft3
1 foot
1 foot
1 ft3
1 foot

12. 15 ft3 15 ft3 15 ft3 Area and Volume 5 feet 3 feet V = Abase * height
= 15 ft2 x 2 ft
= 30 ft3
V = Abase * height
= 15 ft2 x 3 ft
= 45 ft3
15 ft3
15 ft3
1 foot
1 foot
1 ft3
1 foot

13. Area and Volume
V = Abase * height
10 m
3 m
6 m

14. Area and Volume AΔ = bh ÷ 2 AΔ = 3m x 6m ÷ 2 AΔ = 18m2 ÷ 2 AΔ = 9m2
V = Abase * height
3 m
6 m
BASE 
3 m
6 m
10 m
AΔ = bh ÷ 2
AΔ = 3m x 6m ÷ 2
AΔ = 18m2 ÷ 2
AΔ = 9m2
9m2

15. Area and Volume V = Abase * height V = 9m2 x 10 m 9m3 9m3 9m3 9m3
9m3 per “slice” X
10 slices
=90 m3
9m3
9m3
9m3
9m3
9m3
9m3
9m3
9m3
9m3
9m3
3 m
9m3
+ 9m3

16. Find the volume of a cylinder
Area and Volume
Sample Problem:
Find the volume of a cylinder
with a diameter of
3 inches
and
a height
of 5 inches

17. Find the volume of a cylinder with a
Area and Volume
V = Abase * height
Abase
Sample Problem:
Find the volume of a cylinder with a
diameter of 3 inches and
a height of 5 inches
3 in
3 in
Radius = 1.5in
Diameter = 3 in
5 in
Circumference = 3 π in
Area = 2.25 π in2

18. Area and Volume Radius = 1.5in Diameter = 3 in Circumference = 3 π in
V = Abase * height
V = π in2 * height
V = 2.25 π in2 * 5 in
V = π in3
3 in
3 in
Radius = 1.5in
Diameter = 3 in
5 in
Circumference = 3 π in
5 in
Area = 2.25 π in2

19. The area of the base is 2.25 π in2.
Area and Volume
2.25 π in2
2.25 π in3
2.25 π in3
3 in
The area of the base is 2.25 π in2.
The volume of a disc
one inch thick
is 2.25 π in3.
2.25 π in3
V = 2.25 π in3 x 5
V = π in3
2.25 π in3
2.25 π in3
5 in

20. Find the volume of a cylinder with a
Area and Volume
By Formula:
V = Abase * height
V = 2.25 π in2 * 5 in
V = π in3
Find the volume of a cylinder with a
diameter of 3 inches and
a height of 5 inches
3 in
By “Slices”:
Abase = π in2
V slice = π in3
V cylinder = 2.25 π in3 * 5
V = π in3
5 in

21. V = Area of the base * height of the solid
Area and Volume
Definitions
All volume FORMULAS where there is ONE base and triangular sides that come to a single point (like in a pyramid or cone):
V = Area of the base * height of the solid 3
V = Abase * height

22. Try these: 8 cm 6 cm 6 cm 18 cm 5 cm 8 cm 12 cm 6 cm 15 cm
Find the volume of: a) b) c)
8 cm
6 cm
6 cm
18 cm
5 cm
8 cm
12 cm
6 cm
15 cm

23. Try these: 8 cm 6 cm 6 cm 18 cm 5 cm 8 cm 12 cm 6 cm 15 cm a) 240 cm3
Find the volume of: a) b) c)
8 cm
6 cm
6 cm
18 cm
5 cm
8 cm
12 cm
6 cm
15 cm
a) 240 cm3
c) 288 cm3
b) 648 π cm3

24. V = Abase * height 3 Try these: 6 cm 5 cm 18 cm 8 cm 6 cm
Find the volume of: d) e)
6 cm
5 cm
18 cm
8 cm
6 cm
V = Abase * height 3

25. Try these: 6 cm 5 cm 18 cm 8 cm 6 cm d) 80 cm3 e) 216 π cm3
Find the volume of: d) e)
6 cm
18 cm
5 cm
8 cm
6 cm
d) 80 cm3
e) 216 π cm3