10-7 volume of prisms - play with math – exercise...
TRANSCRIPT
Name ________________________________ Date __________________ Class _________________
Practice A Volume of Prisms
Find the volume of each rectangular prism. 1. 2. 3.
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4. 5. 6.
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Find the volume of each triangular prism. 7. 8. 9.
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10. A triangular prism and a rectangular prism have the same lengths, heights, and widths. Which prism has the greater volume?
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11. Tim made a toy chest for his little sister’s square building blocks. If 6 layers of blocks can fit in the box, and each layer has 15 blocks, how many building blocks can the toy chest hold in all?
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LESSON 10-7
Name ________________________________ Date __________________ Class _________________
Practice B Volume of Prisms
Find the volume of each rectangular prism. 1. 2. 3.
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4. 5. 6.
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Find the volume of each triangular prism. 7. 8. 9.
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10. Fawn built a sandbox that is 6 feet long, 5 feet wide, and 12 foot
tall. How many cubic feet of sand does she need to fill the box?
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11. Unfinished lumber is sold in units called board feet. A board foot is the volume of lumber contained in a board 1 inch thick, 1 foot wide, and 1 foot long. How many cubic inches of wood are in 1 board foot?
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LESSON 10-7
Name ________________________________ Date __________________ Class _________________
Practice C Volume of Prisms
Find the volume of each rectangular prism. 1. 2. 3.
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Find the volume of each triangular prism. 4. 5. 6.
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Find the missing measurement for each rectangular prism.
7. ! = ? ; = 34 m; h = 5 m; V = 340 m3 ________________
8. ! = 4.5 ft; = ? ; h = 6 ft; V = 256.5 ft3 ________________
9. ! = 14 yd; = 8 yd; h = ? ; V = 1,344 yd3 ________________
10. ! = ? ; = 1 12 in.; h = 3 12 in.; V = 52 12 in3 ________________
11. A rectangular prism’s base is 8 feet long. It is 2 12 times taller
than it is long and 12 as wide as it is tall. What is the volume
of that prism? _________________ 12. A rectangular box is 3 feet wide, 6 feet long, and 4 feet tall.
Inside the box, Phil placed a triangular prism that is 3 feet tall, and has a base 2 feet wide with a height of 5 feet. If he places another triangular prism of the same size in the box, how much empty space will there be in the box? _________________
LESSON 10-7
Name ________________________________ Date __________________ Class _________________
Review for Mastery Volume of Prisms
Volume is the number of cubic units needed to fill a space. To find the volume of a rectangular prism, first find the area of the base.
length = 3 units width = 2 units A = ! = 3 • 2 = 6 square units.
The area of the base tells you how many cubic units are in the first layer of the prism.
Next, multiply the result by the number of layers in the prism. The prism has 4 layers, so multiply 6 by 4.
6 • 4 = 24
So, the volume of the rectangular prism is 24 cubic units.
Find the volume of each rectangular prism. 1. 2.
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To find the area of a triangular prism, first find the area of the base. A = 12 bh
= 12 (5 • 4)
= 10 square units Then multiply the result by the height of the prism.
10 • 3 = 30 The volume of the triangular prism is 30 cubic units.
Find the volume of each triangular prism. 3. 4.
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LESSON 10-7
Name ________________________________ Date ___________________ Class __________________
Challenge Fish Tank Math
Did you know that most fish grow according to the size of their tank? In fact, a freshwater fish needs about 1 gallon of water for every inch of its body. The volume of 1 gallon of water is about 231 in3. So, a fish tank with a volume of a 700 in3 will hold 700 ⎟ 231 ≈ 3 gallons of water. This size tank would be the healthiest home for a 3-inch-long fish.
Find the volume of each fish tank. Then match each fish to the best tank for it.
Volume of Tank: ____________________ Volume of Tank: ____________________
Gallons of Water: ____________________ Gallons of Water: ____________________
Fish: ____________________ Fish: ____________________
Volume of Tank: ____________________ Volume of Tank: ____________________
Gallons of Water: ____________________ Gallons of Water: ____________________
Fish: ____________________ Fish: ____________________
LESSON 10-7
Name ________________________________ Date __________________ Class _________________
Problem Solving Volume of Prisms
Write the correct answer. 1. At 726 feet tall, Hoover Dam is one
of the world’s largest concrete dams. In fact, it holds enough concrete to pave a two-lane highway from New York City to San Francisco! The dam is shaped like a rectangular prism with a base 1,224 feet long and 660 feet wide. About how much concrete forms Hoover Dam?
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3. Benitoite, a triangular prism crystal, is the official state gem of California. One benitoite crystal found in California is 1.2 cm tall, with a base width of 2 cm and a base height of 1.3 cm. How many cubic centimeters of benitoite are in that crystal?
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2. The Vietnam Veterans Memorial in Washington, D.C., is a 493.5-foot- long wall made of polished black granite engraved with the names of soldiers who died in the war. The wall is 0.25 feet thick and has an average height of 9 feet. About how many cubic feet of black granite was used in the Vietnam Veterans Memorial?
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4. The Flatiron Building in New York City is a triangular prism. A solid bronze souvenir model of the building is 5 inches tall, with a base height of 1.5 inches and a base width of 2.5 inches. How much bronze was used to make the model?
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Circle the letter of the correct answer. 5. Individual slices of pizza are sold in
2-inch-tall triangular prism boxes. The box base is 8 inches wide, with a 7-inch height. How many cubic inches of pizza will fit in each box? A 112 in3 C 60 in3 B 102 in3 D 56 in3
7. A box can hold 175 cubic inches of cereal. If the box is 7 inches long and 2.5 inches wide, how tall is it? A 25 in. B 10 in. C 17.5 in. D 9.5 in.
6. The world’s largest chocolate bar is a huge rectangular prism weighing more than a ton! The bar is 9 feet long, 4 feet tall, and 1 foot wide. How many cubic feet of chocolate does it have? F 13 ft3 H 36 ft3 G 14 ft3 J 72 ft3
8. A triangular prism used to reflect light is made of 120 cm3 of glass. If the prism is 5 centimeters tall, what is the area of each of its triangular bases? F 24 cm G 12 cm
H 12 cm2
J 24 cm2
LESSON 10-7
Name ________________________________ Date __________________ Class _________________
Reading Strategies Analyze Information
The volume of a prism is the number of cubic units it contains.
Look at the first layer of cubic units in this rectangular prism.
1. How many cubes long is the first layer? _________________________
2. How many cubes wide is the first layer? _________________________
3. How many cubes are in the first layer? _________________________
Now look at the next layer of cubes.
4. How many cubes long is the top layer? _________________________
5. How many cubes wide is the top layer? _________________________
6. How many cubes are in the top layer? _________________________
7. What is the total number of cubes in both layers? _________________________
8. What is the total volume of the rectangular prism? _________________________
LESSON 10-7
Name ________________________________ Date __________________ Class _________________
Puzzles, Twisters & Teasers 3D Match
Find the volume of each of the prisms below. Draw a line to the correct answer. Rearrange the answer letters to solve the riddle. 1.
2.
3.
4.
5.
What grows the more you take away?
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LESSON 10-7
L 297 cm3 C 148.5 cm3 G 43 cm3 H 96 cm3 A 19 cm3
M 161.5 cm3 O 80.75 cm3 S 30.25 cm3 E 1120 cm3 K 560 cm3
Name ________________________________ Date __________________ Class _________________
CODE
61007 Answers
LESSON 10-7
Practice A 1. V = 27 in3 2. V = 24 ft3 3. V = 960 yd3 4. V = 210 m3 5. V = 125 cm3 6. V = 540 yd3 7. V = 60 cm3 8. V = 27 in3 9. V = 80 m3
10. the rectangular prism 11. 90 building blocks
Practice B 1. 857.375 in3 2. 1,800 ft3 2. 6,800 yd3 4. 231.556 m3 5. 980 yd3 6. 3,511.808
cm3 7. 910 cm3 8. 73.5 ft3 9. 22,500 in3 10. 15 ft3 11. 144 cubic inches of wood
Practice C
1. 274 5
8 in3 2. 0.48 m3
3. 98 9
32 ft3 4. 1,137.4425
cm3
5. 17 119
128 ft3 6. 0.02275 m3
7. 2 m 8. 9.5 ft 9. 12 yd 10. 10 in. 11. 1,600 ft3 12. 42 ft3
Review for Mastery 1. 16 square units 2. 30 square
units
3. 16 square units 4. 15 square units
Challenge 5,760 in3; about 25; koi goldfish 2,970 in3; about 13; clown loach 1,170 in3; about 5; redtail shark 1,600 in3; about 7; angelfish
Problem Solving 1. about 586,491,840 ft3 of concrete 2. about 1,110.375 ft3 of black granite 3. 1.56 cm3 of benitoite 4. 9.375 in3 of bronze 5. D 6. H 7. B 8. J
Reading Strategies 1. 4 cubes 2. 3 cubes 3. 12 cubes 4. 4 cubes 5. 3 cubes 6. 12 cubes 7. 24 cubes 8. 24 cubic units
Puzzles, Twisters & Teasers
A HOLE