This worksheet gives Grade 6 students ten problems on the volume of rectangular prisms, including prisms with fractional edge lengths and packing with unit cubes. The problems start with whole-number edges and move toward missing dimensions and mixed numbers.
The last three problems are word problems about a fish tank, shipping boxes, and a sandbox. Every problem practices Common Core standard 6.G.A.2. Write each formula, show the substitution, and label every answer in cubic units.
Problem 1: Whole-number edges
Find the volume of a rectangular prism that is \(6\text{ ft}\) long, \(4\text{ ft}\) wide, and \(3\text{ ft}\) tall.
Problem 2: Box volume
Find the volume of a box with length \(7\text{ in}\), width \(5\text{ in}\), and height \(2\text{ in}\).
Problem 3: Base area times height
A prism has a base area of \(24\text{ in}^2\) and a height of \(5\text{ in}\). Find its volume.
Problem 4: Fractional width
Find the volume of a prism that is \(4\text{ in}\) long, \(\frac{1}{2}\text{ in}\) wide, and \(3\text{ in}\) tall.
Problem 5: Packing with cubes
A prism is \(1\text{ in}\) long, \(\frac{3}{4}\text{ in}\) wide, and \(\frac{1}{2}\text{ in}\) tall. It is packed with cubes that have edges of \(\frac{1}{4}\text{ in}\). (a) How many cubes fit? (b) What is the volume of one cube? (c) What is the volume of the prism?
Problem 6: Missing height
A prism has a volume of \(150\text{ ft}^3\), a length of \(10\text{ ft}\), and a width of \(5\text{ ft}\). Find its height.
Problem 7: Mixed-number edges
Find the volume of a prism that is \(2\frac{1}{2}\text{ ft}\) long, \(1\frac{1}{2}\text{ ft}\) wide, and \(2\text{ ft}\) tall.
Problem 8: Aquarium
Jamal’s fish tank is a rectangular prism \(20\text{ in}\) long, \(10\text{ in}\) wide, and \(12\text{ in}\) tall. The water is \(9\text{ in}\) deep. Find the volume of the water, and then the volume of water that must be added to fill the tank.
Problem 9: Storage boxes
Shipping boxes are \(2\frac{1}{2}\text{ ft}\) by \(2\text{ ft}\) by \(1\frac{1}{2}\text{ ft}\). A storage space is \(10\text{ ft}\) by \(6\text{ ft}\) by \(3\text{ ft}\). How many boxes fit in the space with no gaps?
Problem 10: Sandbox
A sandbox is \(6\text{ ft}\) long and \(4\frac{1}{2}\text{ ft}\) wide. Maya fills it with sand to a depth of \(\frac{3}{4}\text{ ft}\). Sand costs \(\$4\) per cubic foot. Find the volume of sand and the total cost.
See every chapter on the Grade 6 math page.