# Volume of cubes and cuboids

Videos, worksheets, solutions, and activities to help Grade 6 students learn how to solve word problems in Singapore Math.

In this lesson, we will learn how to solve word problems involving the volume of cubes and cuboids.

Grade 6: Volume of Cubes and Cuboids, Problem 1
Find one dimension of a cuboid given its volume and the other dimensions
Grade 6: Volume of Cubes and Cuboids, Problem 2
Find the length of one edge of a cube given its volume.
Example: The volume of the Rubik's cube below is 216 cm3. What is the length of one edge of the cube?

Grade 6: Volume of Cubes and Cuboids, Problem 3
How much more to add to fill up the container?
Example: A rectangular container with a base area of 200 cm2 is filled with water to a height of 15 cm. If the container has a height of 20 cm, how much water (in liters) should be added to it to fill it completely?
Grade 6: Volume of Cubes and Cuboids, Problem 4
Find the height of a cuboid given its volume and base area.
Example: Josh built a rectangular cardboard box 18 cm high with a square base and a volume of 2178 cm3. Then he realized he did not need a box that large, so he chopped off the height of the box reducing its volume to 1331 cm3. Was the new box cubical?

Grade 6: Volume of Cubes and Cuboids, Problem 5
Solving a word problem involving ratio and volume of a cuboid.
Example: A rectangular juice dispenser has a base area of 450 cm2 and a height of 25 cm. Gale adds syrup and water in the ratio 1:3 to the dispenser to make a beverage. If he uses 6.75 liters of water, what percentage of the dispenser will be filled when the beverage is made?
Grade 6: Volume of Cubes and Cuboids, Problem 6
Solving a word problem involving fractions and volume of a cuboid.
Example: A rectangular aquarium, is 2/5 filled. When 16 liters of water are added, the aqurium is 2/3 filled. Find the height of the aquarium if its length and width are 50 cm and 40 cm respectively.

Grade 6: Volume of Cubes and Cuboids, Problem 7
Finding the height of a cuboid given its volume and base area.
Example: The water level in a rectangular tank, 65 cm long and 45 cm wide, is 14 cm. It will take another 58.5 liters of water to fill the tank to its brim. Find the height of the tank.
Grade 6: Volume of Cubes and Cuboids, Problem 8
Solving a word problem on volume involving cuboids of various sizes.
Containers A (6cm, 5cm, 4cm), B (5cm, 4cm, 3 cm) and C (3cm, 3cm, 2 cm) are three rectangular containers. At first, container A is filled with water to its brim while containers B and C are empty. Next, some water from container A is poured into containers B and C so that container B is completely full while container C is half full. Find the height of the water left in container A.

Grade 6: Volume of Cubes and Cuboids, Problem 9
Solving a word problem involving percentage and volume of a cuboid.
Example: A rectangular vase with a square base and 25 cm height is filled with water to its maximum capacity of 1.6 liters. Shelley puts some marbles into the vase causing 235 ml of water to spill. Then she removes all the marbles from the vase causing a further spillage of 85 ml of water. What is the height of the water level in the vase now?
Grade 6: Volume of Cubes and Cuboids, Problem 10
Solving a word problem involving rates of flow of water and volume of a cuboid.
Example: An empty rectangular bath tub 150 cm long, 60 cm wide and 500 cm high is being filled with water from a tap at a rate of 30 liters per minute. The tap is turned off after 12 minutes. Water is then drained out of the tub at a rate of 18 liters per minute. What would be the drop in the water level (measured in cm) 6 minutes later?

Grade 6: Volume of Cubes and Cuboids, Problem 11
Solving a word problem involving rates of inflow and outflow of water and volume of a cuboid.
Example: At 9 am, Kate turned on the supply tap which dispensed water at a rate of 3 liters per minute to fill an empty rectangular container. At the same time, water began leaking out of the container at a rate of 0.5 liters per minute through its faulty tap. Kate turned off the supply tap when the container was filled to its capacity. Given that the container measured 20 cm by 15 cm by 25 cm, at what time was the container completely empty again.

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