Volume of Rectangular Prism Worksheet

Volume and surface area formulas

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The key is worked out with whole-number arithmetic from the lengths printed on each drawing, so an answer is exact: a whole number, a decimal that ends, or a multiple of π. With 3.14 for π an answer is rounded to the nearest hundredth only when it has to be, and the key marks it with ≈.

Solid	Volume	Surface area
Cube	V = s³	SA = 6s²
Rectangular prism (cuboid)	V = l × w × h	SA = 2(lw + lh + wh)
Triangular prism	V = area of the triangle × length	SA = 2 triangles + 3 rectangles
Cylinder	V = πr²h	SA = 2πr² + 2πrh
Square pyramid	V = ⅓ × b² × h	SA = b² + 2bs, where s is the slant height
Cone	V = ⅓πr²h	SA = πr² + πrs, where s is the slant height
Sphere	V = 4/3 × πr³	SA = 4πr²

Every sheet has a short code, printed at the foot of the sheet and of its answer key. A share link brings the same sheet back, figure for figure, so a key printed later still fits the copies you handed out.

How it works

This free volume of rectangular prism worksheet has 8 problems on 1 page: 4 blocks of unit cubes to count, 4 rectangular prisms to multiply. For a volume of cube worksheet, leave only Cubes lit under On the sheet.

Read the full guide

From counting cubes to l × w × h

Count unit cubes draws a block with its faces ruled into unit cubes, 2 to 6 long, up to 4 deep and 5 high. The key gives the count as a product: V = 24 cubic units (3 × 2 × 4). Rectangular prisms labels all three edges, none over 12 units, and never draws a cube.

Decimals, units, a missing edge

Lengths swaps Whole numbers for One decimal. At most two edges of a prism carry a decimal, so answers stop at two places: 8.5 × 3.7 × 10 = 314.5. Units sets cm, m, in or ft. Missing dimension prints V = 336 cm³ above the drawing and marks one edge h = ?. The key divides: h = 7 cm (336 ÷ (8 × 6)). Every third problem asks for a cube's edge.

On the counting blocks, ask for one layer, then the layers: 6 × 4 = 24. That is V = b × h.
The key prints the factors, (3 × 6 × 10), so a misread edge shows up apart from a multiplication slip.
Keep Lengths on Whole numbers while Cubes is lit: an edge of 2.6 gives 2.6 × 2.6 × 2.6 = 17.576.

Questions and answers

How do you find the volume of a rectangular prism?

Multiply length by width by height. A prism 3 cm long, 6 cm wide and 10 cm high has a volume of 3 × 6 × 10 = 180 cm³. Base area times height agrees: 18 × 10. The unit is cubic because the answer counts cubes.

What grade is volume of rectangular prisms?

Grades 5 and 6. Common Core 5.MD.4 has students measure volume by counting unit cubes, and 5.MD.5 applies V = l × w × h to whole-number edges. In grade 6, 6.G.2 moves to fractional edge lengths. This page prints decimals, not fractions.

How do you find the volume of a cube?

Multiply the edge length by itself, then by itself again: V = s × s × s. A cube with 7 cm edges holds 7 × 7 × 7 = 343 cm³. With only Cubes lit, a sheet of 9 deals 9 different edges from 2 to 12 units.