Name ______________________________ Date ...



Name ________________________________________ Date ____________________

Volume Formula – Rectangular Prisms

I. Find the volume of the following rectangular prisms.

1.

|Length (l) |Width (w) |Height (h) |Process Column |Volume |

| | | | |(in cubic units) |

|3 |3 |3 |3x3x3 |27 cm3 |

2.

|Length (l) |Width (w) |Height (h) |Process Column |Volume |

| | | | |(in cubic units) |

|4 |3 |5 |4x3x5 |60cm3 |

Volume Formula: ____________________

2)

II. Find the area of each base from above.

a.) 4.5 cm2 b.) 20cm2 c.) 16 cm2

3. How did you figure out the area of the base of your prisms?

Length times width

4. Is the area of each base the same as the volume of each prism? Yes or No? Explain.

you have to multiply the area of the base with the height

5. What is the volume of each prism from above?

a.) 18 cm3 b.) 20cm3 c.) 96 cm3

III. Calculate the volume of each rectangular prism.

Volume Formula: ______________

Volume Formula: ______________

7)

8. A tunnel is being built through a small hill. It will be 10 ft tall and 15 ft wide. A diagram of

the tunnel is shown below.

Which of the following is the best estimate of the volume of the tunnel?

A. 9000 ft[pic] B. 4000 ft[pic] C. 6000 ft[pic] D. 9000 ft[pic]

9. Matt’s aquarium is shaped like a rectangular prism. The base of his tank has an area of

59.8 square feet. If the water level is at a height of 9 feet, what is the volume of the water

in the tank?

A. 68.8 cu. ft. B. 538.2 cu. ft. C. 518.2 cu. ft. D. 1076.4 cu. ft.

Developing Volume Formula – Triangular Prisms

I. Area of Triangles Review

10. Find the area for each triangle below:

Formula for Area of a Triangle: _______________

Answer ___________ Answer ___________ Answer ___________

Answer = 4 sq ft Answer = 12 sq ft Answer = 10 sq ft

11. Which components of a triangular prism make-up the base of the prism?

Triangle

12. How can you distinguish between the height of a triangular prism and height of the base of

the prism? The height is the distance between the two triangle bases.

II. Volume of Triangular Prisms

Formula for area of the base of a triangular prism: ½ Bh

13.

14.

15. A camping tent has the shape of the triangular prism below. What is the size of the tent in

cubic feet?

16. A triangular prism has a volume of 100cm[pic] and a height of 25cm. Find the area of its base.

17. A rectangular box has a volume of 8856 cm[pic]. The length of the box is 24.6 cm. The

width of the box is 18 cm. Find the height. 20cm

18. The volume of a cylinder is 15,700 cm[pic]. The area of the base is 628 cm[pic]. What is the

height? 25 cm

19. The volume of a cylinder is 3.14 m[pic]. Its height is 1 m. Find the radius and diameter of the

cylinder.

Radius _______1 Diameter _____2

20. A cube has a volume of 64 cubic centimeters. What is the length of each edge of the

cube? 4cm

21. A watering trough for horses has the shape of the triangular prism below. How much

water will the trough hold?

22. The sand level in the sandbox is 4 inches below the top of the sandbox. The bottom of

the box takes 1728 square inches of space. The height of the sandbox is 12 inches.

Which process below could be used to calculate the volume of the sand?

A. [pic] V = 1728 + 12 C. V = 1728 [pic] 4 [pic]12

B. V = (1728)(12) D. V = 1728 (12 - 4)

-----------------------

Review of 6th Grade Skills

3 cm

3 cm

3 cm

5 cm

3 cm

4 cm

4 cm

6 cm

1.5 cm

a.)

4 cm

b.)

c.)

2 cm

1 cm

4 cm

3 cm

10 cm

To calculate the volume of a rectangular prism, you can use:

V = _________ or

V = _________

6.

|Area of Base (B) |Height of Prism (h) |Process |Volume |

| | |Column |(in cubic units) |

|24 |2 |24x2 |48cm3 |

Base area = 24 in2

Height = 2 in

Explain 3 ways to find the volume of this prism:

a.)count the blocks

b.)find area of base, multiply by height

c.)find area of front, multiply by depth

60 ft

3 feet

8 feet

4 ft

5 ft

4 ft

2 ft

[pic]

Base area = 24 in2

Height = 2.5 in

|Area |Height |Process |Volume |

|of Base (B) |of Prism (h) |Column |(in cubic units) |

|24 |2.5 |24x2.5 |60in3 |

[pic]

b =6 cm

h =2 cm

h =4 cm

|Area |Height |Process |Volume |

|of Base (B) |of Prism (h) |Column |(in cubic units) |

|12 |2 | |24cm3 |

12 ft

4[pic] ft

5 ft

A. 135 ft[pic] C. 21.5 ft[pic]

B. 270 ft[pic] D. 135 ft[pic]

A. 75 cm[pic] C. 125cm[pic]

B. 4 cm[pic] D. 25 cm[pic]

3 ft

A. 48 ft[pic] C. 86 ft[pic]

B. 96 ft[pic] D. 192 ft[pic]

4 ft

8 ft

12 in.

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