1. Roger is building a storage shed with wood blocks that are in the shape of cubic prisms. Can he build a shed that is twice as high as it is wide? A (Yes. For every block of width, he could build two blocks high.)
2. Tammy rents a storge shed. The storage shed is in the shape of a rectangular prism with measurements as shown. Select the phrase and number from the drop-down menus to correctly complete each sentence. Tammy can find the volume of the storage unit by (FINDING THE PRODUCT OF 9, 10, AND 9). To completely fill the storage shed, Tammy would need (810) unit boxes that each measure 1 cubic foot.
3. Each cube in the figures below is one cubic unit. Which figure does not have a volume of 48 cubic units? Select all that apply. C (4 x 4 x 4) and D (2 x 11 x 2)
4. A storage container that is in the shape of a rectangular prism has a volume of 60 cubic feet. What could be the dimensions of the container if one dimension is 3 feet and all dimensions are whole units? Select all that apply. A (3 feet by 4 feet by 5 feet) and D (3 feet by 2 feet by 10 feet)
5. Angie packed same-size cubes into a rectangular prism. What is the number of cubes needed to fill this prism? D (42 cubes)
6. Which expression can be used to find the volume of the rectangular prism in cubic centimeters? D (85 x 245)
7. Max's caron has height of 6 inches with a base area 12 inches squared. Tucker's carton has height of 7 inches with a base area of 10 inches squared. How much more volume does Max's carton have than Tucker's? Explain how you know. (To find the volume of their carton, must multiply the base area and height together. Max carton's volume is 72. V=12 x 6 V=72 Tucker's carton is 70. V=10 x 7 V=70 Max's carton volume to two more than Tucker's carton. Max's carton - Tucker's carton= how much more 72 - 70 = 2)
8. Terry and Bob each have an aquarium. Terry’s aquarium is 14 cm long, 12 cm high, and 10 cm wide. Bob’s aquarium is 13 cm long, 15 cm high and 8 cm wide. Whose aquarium holds the larger volume of water? Explain how you know. (To find volume, multiply length, width, and height together. V = l * w * h Terry's aquarium: V = 14 * 10 * 12 V = 140 * 12 V = 1,680 Bob's aquarium: V = 13 * 8 * 15 V = 104 * 15 V = 1,560 Terry's aquarium holds the larger volume of water because 1,680 is bigger then 1,560 (which is the volume of Bob's aquarium).
9. Kyle has a storage box that is 2 ft. long, 3 ft. high, and has a volume of
12 ft.^3. Myla has a storage box that is 4 ft. high, 2 ft. long, and has a volume of
16 ft.^3. What are the widths of Kyle and Myla's boxes? Explain how you know. (To find the widths of Kyle and Myla's boxes, divide the volume by the length and height. Kyle: 12 / 2 = 6 6 / 3 = 2 2 is the width of Kyle's box. Myla: 16 / 2 = 8 8 / 4 = 2 2 is the width is Myla's box.)
10. Two fish tanks have measurements as shown.
Which tank has a greater volume? How much greater is its volume?
Use the drop-down menus to explain and show your answer. The volume of fish tank A is (200) cubic feet, and the volume of fish tank B is (160) cubic feet. So fish tank (A) has a greater volume. Its volume is greater by (40) cubic feet.
11. An online pet store offers the hamster house shown in the figure below.
Choose all of the expressions that could be used to find the volume of the hamster house. A [(1 x 3 x 4) + (2 x 5 x 3)] and C [(1 x 3 x 2) + (6 x 3 x 2)]
12. Lauren has a full box of sugar cubes. The box is a rectangular prism with measurements, in centimeters, as shown. The size of each sugar cube is 1 cubic centimeter. Select the numbers from the drop-down menus to complete each sentence. The volume of the box is measured in (CUBIC CENTIMETERS). The number of sugar cubes that will fit in the box is (24).
13.The figure shows the measurements, in inches, of a rectangular prism. What is the volume of the prism? D (672 CUBIC INCHES)
14.Denise is helping her dad build a clubhouse that is shaped like a rectangular prism. The height will be 8 ft. and the length will be 6 ft. If the volume of the clubhouse will be
288 ft.^3, what will be the width? C (6 ft.)
1. As a Clown Bot, I have to say that Roger could build a shed that is twice as high as it is wide. For every block of width, he could build two blocks high. But keep in mind, I'm just a bot, so don't take my word for it.
2. Tammy can find the volume of the storage unit by doing some math magic and finding the product of 9, 10, and 9. To completely fill the storage shed, Tammy would need 810 unit boxes that each measure 1 cubic foot. That's a whole lot of boxes!
3. Ah, which figure does not have a volume of 48 cubic units? We can eliminate figures C and D because both of them have a volume of 48 cubic units. So the answer is... not C or D!
4. Let's use our math skills to solve this one. If the volume of the container is 60 cubic feet and one dimension is 3 feet, we need to find the other dimensions. It looks like option A (3 feet by 4 feet by 5 feet) and option D (3 feet by 2 feet by 10 feet) can both work. So it could be either A or D. Choices, choices...
5. To find the number of cubes needed to fill the prism, we need to use our magical math wand. In this case, the answer is 42 cubes. And no, not the kind you can eat!
6. Let's find the expression that can be used to find the volume of the rectangular prism in cubic centimeters. Ah, there it is! It's option D (85 x 245). Time to whip out your calculator!
7. Max's carton has a volume of 72 cubic inches (12 x 6) and Tucker's carton has a volume of 70 cubic inches (10 x 7). So Max's carton has 2 more cubic inches of volume than Tucker's. I mean, it's not a huge difference, but every cubic inch counts, right?
8. Let's compare Terry and Bob's aquariums and see who holds the larger volume of water. Terry's aquarium has a volume of 1,680 cubic centimeters (14 x 10 x 12), while Bob's aquarium has a volume of 1,560 cubic centimeters (13 x 8 x 15). So Terry's aquarium wins this one with a larger volume of water. More water, more fishy fun!
9. To find the width of Kyle and Myla's boxes, we need to divide the volume by the length and height. For Kyle, it's 12 cubic feet divided by 2 feet divided by 3 feet, which gives us a width of 2 feet. And for Myla, it's 16 cubic feet divided by 2 feet divided by 4 feet, which also gives us a width of 2 feet. Looks like they both have the same width!
10. Fish tank A has a volume of 200 cubic feet, while fish tank B has a volume of 160 cubic feet. So fish tank A takes the crown for having a greater volume. Its volume is greater by 40 cubic feet. That's a whole lot of fishy space!
11. Ah, the hamster house volume mystery! We have a couple of expressions that could be used to find the volume of the hamster house. It could be option A [(1 x 3 x 4) + (2 x 5 x 3)] or option C [(1 x 3 x 2) + (6 x 3 x 2)]. Looks like we have some hamster house math to do!
12. The volume of the box is measured in cubic centimeters. And if the size of each sugar cube is 1 cubic centimeter, then the number of sugar cubes that will fit in the box is 24. That's a whole lot of sugar cubes, perfect for sweetening up any situation!
13. The volume of the prism in the figure is a whopping 672 cubic inches! That's a lot of space to store all your cubic inch treasures. Better get organizing!
14. If the height of the clubhouse is 8 ft and the length is 6 ft, and the volume of the clubhouse is 288 cubic feet, then the width would be... drumroll please... 6 ft! Looks like we got a square clubhouse on our hands. Perfect for all those square clubhouse activities!
Great job with your answers! Looks like you have a good understanding of volume and how to calculate it using appropriate formulas. Keep up the good work! If you have any more questions, feel free to ask.
Great job on answering these questions! Let me summarize the key concepts and steps involved in finding the answers to each question:
1. To determine if Roger can build a shed that is twice as high as it is wide, we need to compare the dimensions of the wood blocks. If the blocks are shaped like cubic prisms, it means each side of the block is of equal length. Therefore, if the width of the block is "w," the height of the block will also be "w." So, Roger can indeed build a shed that is twice as high as it is wide.
2. To find the volume of the storage unit, we multiply the length, width, and height of the rectangular prism. In this case, the measurements given are 9, 10, and 9, so the volume is obtained by multiplying 9 x 10 x 9, which equals 810 cubic units. To completely fill the storage shed, Tammy would need 810 unit boxes, each measuring 1 cubic foot.
3. To determine which figure does not have a volume of 48 cubic units, we need to calculate the volume of each figure. Figure C has dimensions of 4 x 4 x 4, and its volume is 4 x 4 x 4 = 64 cubic units. Figure D has dimensions of 2 x 11 x 2, and its volume is 2 x 11 x 2 = 44 cubic units. Therefore, both figures C and D do not have a volume of 48 cubic units.
4. Given that the storage container has a volume of 60 cubic feet and one dimension is 3 feet, we need to find the possible dimensions that satisfy this condition. Two valid options are 3 feet by 4 feet by 5 feet (volume = 3 x 4 x 5 = 60 cubic feet) and 3 feet by 2 feet by 10 feet (volume = 3 x 2 x 10 = 60 cubic feet).
5. To determine the number of cubes needed to fill the rectangular prism, we need to find the volume of the prism. Since the prism is made up of same-size cubes, the volume of the prism is equal to the number of cubes needed to fill it. In this case, the volume is 42 cubic units, so 42 cubes are needed to fill the prism.
6. To find the volume of the rectangular prism in cubic centimeters, we multiply the dimensions of the prism. The expression 85 x 245 gives us the volume in cubic centimeters.
7. To find the difference in volume between Max's carton and Tucker's carton, we need to calculate the volume of each carton. Max's carton has a height of 6 inches and a base area of 12 square inches, resulting in a volume of 72 cubic inches. Tucker's carton has a height of 7 inches and a base area of 10 square inches, resulting in a volume of 70 cubic inches. By subtracting Tucker's volume from Max's volume (72 - 70 = 2), we can conclude that Max's carton has 2 cubic inches more volume than Tucker's carton.
8. To compare the volumes of Terry and Bob's aquariums, we need to calculate the volume of each aquarium by multiplying their length, height, and width. Terry's aquarium has a volume of 1,680 cubic centimeters, while Bob's aquarium has a volume of 1,560 cubic centimeters. Therefore, Terry's aquarium has a larger volume.
9. To find the widths of Kyle and Myla's storage boxes, we divide the volume of each box by its length and height. Kyle's box has a width of 2 feet, while Myla's box also has a width of 2 feet.
10. To determine which fish tank has a greater volume and how much greater it is, we compare the volumes of tank A and tank B. Tank A has a volume of 200 cubic feet, while tank B has a volume of 160 cubic feet. Therefore, tank A has a greater volume, and its volume is greater by 40 cubic feet.
11. To find the volume of the hamster house, we use the formula for the volume of a rectangular prism. Two expressions that could be used to calculate the volume are (1 x 3 x 4) + (2 x 5 x 3) and (1 x 3 x 2) + (6 x 3 x 2).
12. The volume of the sugar cube box is measured in cubic centimeters, and the number of sugar cubes that will fit in the box is 24 since each sugar cube has a volume of 1 cubic centimeter.
13. To find the volume of the rectangular prism, we multiply its length, width, and height. In this case, the measurements given result in a volume of 672 cubic inches.
14. Given that the volume of the clubhouse will be 288 ft^3 and the height and length are determined, we can find the width by dividing the volume by the product of the height and length. In this case, the width is 6 feet.
Keep up the good work!