Volume of Rectangular Prisms: Grade 6 Math Test – PDF Download

Question 1: Whole-number edges (2 points)

1. Find the volume of a box that is \(9\text{ in}\) long, \(4\text{ in}\) wide, and \(6\text{ in}\) tall. (1 point)
2. Find the volume of a prism with a base area of \(35\text{ ft}^2\) and a height of \(4\text{ ft}\). (1 point)

Question 2: Fractional edges (2 points)

A prism has a length of \(\frac{3}{4}\text{ ft}\), a width of \(\frac{1}{2}\text{ ft}\), and a height of \(4\text{ ft}\). Find its volume.

Question 3: Cube packing (3 points)

A rectangular prism is packed with cubes that have edges of \(\frac{1}{2}\text{ in}\). The prism holds 3 cubes along its length, 2 cubes along its width, and 1 layer.

1. Find the length, width, and height of the prism. (1 point)
2. Find the volume by counting cubes. (1 point)
3. Find the volume by multiplying the edge lengths. (1 point)

Question 4: Missing height (2 points)

A rectangular prism has a volume of \(84\text{ ft}^3\), a length of \(7\text{ ft}\), and a width of \(4\text{ ft}\). Find its height.

Question 5: Fish tank (3 points)

A fish tank is \(30\text{ in}\) long, \(12\text{ in}\) wide, and \(15\text{ in}\) tall. The water is \(10\text{ in}\) deep.

1. Find the volume of the tank. (1 point)
2. Find the volume of the water. (1 point)
3. Find the volume of water that must be added to fill the tank. (1 point)

Question 6: Packing crates (3 points)

A crate is \(6\text{ ft}\) long, \(3\text{ ft}\) wide, and \(3\text{ ft}\) tall. It is packed with cube-shaped boxes that have edges of \(1\frac{1}{2}\text{ ft}\).

1. Find the volume of the crate. (1 point)
2. Find the volume of one box. (1 point)
3. Find how many boxes fit in the crate. (1 point)

Question 7: Compare prisms (2 points)

Prism A is \(5\text{ ft}\) by \(4\text{ ft}\) by \(3\text{ ft}\). Prism B is \(6\text{ ft}\) by \(2\frac{1}{2}\text{ ft}\) by \(5\text{ ft}\). Which prism has the greater volume, and by how much?

Question 8: Sandbox sand (3 points)

A sandbox is \(8\text{ ft}\) long and \(5\text{ ft}\) wide. Aisha fills it with sand to a depth of \(\frac{3}{4}\text{ ft}\). Sand is sold in bags of \(1\frac{1}{2}\text{ ft}^3\) for \(\$7.25\) per bag.

1. Find the volume of sand needed. (1 point)
2. Find the number of bags needed. (1 point)
3. Find the total cost. (1 point)

See every chapter on the Grade 6 math page.