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Geometry and measurementGrades 5–7

Surface area and volume worksheets

Prints drawn 3D solids with labeled edges and asks for volume, surface area or both. Choose rectangular prisms, cubes, cylinders or a mix, from 2 to 12 problems per sheet, and print the sheet with a worked answer key.

By Paul Gunder. Free to print for home, classroom and office use; see how our printables are made.

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Surface Area and Volume of Rectangular Prisms2 pages, answer key from page 2 · US Letter

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NameDateScoreSurface Area and Volume of Rectangular PrismsVolume = length × width × height. Surface area = 2(lw + lh + wh): add the areas of all six faces. Write cubic unitsfor volume and square units for area.1.9 ft6 ft10 ftV = __________ SA = __________2.10 in2 in11 inV = __________ SA = __________3.8 ft12 ft7 ftV = __________ SA = __________4.7 m8 m10 mV = __________ SA = __________5.10 in9 in7 inV = __________ SA = __________6.11 ft6 ft11 ftV = __________ SA = __________PrintablePal.com · free printablesSurface Area and Volume of Rectangular Prisms
Worksheet, page 1
Surface Area and Volume of Rectangular Prisms: answer key1.9 ft6 ft10 ftV = __________ SA = __________V = 540 ft³ SA = 408 ft²2.10 in2 in11 inV = __________ SA = __________V = 220 in³ SA = 304 in²3.8 ft12 ft7 ftV = __________ SA = __________V = 672 ft³ SA = 472 ft²4.7 m8 m10 mV = __________ SA = __________V = 560 m³ SA = 412 m²5.10 in9 in7 inV = __________ SA = __________V = 630 in³ SA = 446 in²6.11 ft6 ft11 ftV = __________ SA = __________V = 726 ft³ SA = 506 ft²PrintablePal.com · free printablesAnswer key
Answer key, page 1

On this page

Two measurements, one box

Volume tells you how much a solid holds, counted in cubes. Surface area tells you how much wrapping paper would cover it, counted in squares. Students often swap the two because both start from the same three measurements. Printing them as a pair on the same drawing lets them practice telling the difference.

Rectangular prisms are the starting point on this page (the preset), which fits grades 5 to 7. Students should already be comfortable multiplying three numbers and finding rectangle area. If a cylinder is the goal, the companion page on surface area of cylinders focuses on that solid alone.

What each problem looks like

A box is drawn in a slanted view with its length along the bottom, its height on the left and its width on the receding side, each marked with a number and a unit (centimeters, meters, inches or feet). Dimensions run from 2 to 12. A cube shows its edge on each of the three labels. Two drawings appear per row, each with an answer line underneath. The instruction line gives both formulas.

Choosing the settings

  • Solids. Rectangular prisms, cubes, cylinders, or a mix. The preset is prisms.
  • Find. "Volume," "Surface area," or both. With "Volume and surface area" each drawing gets two blanks, V and SA. Use a single measurement at first, then both once each is solid.
  • Cylinder answers. Applies only to cylinders: use 3.14 and round to tenths, or leave in terms of π. It has no effect on prisms and cubes.
  • Number of problems. Six is a standard page; four if you want students to show full working.

Answers on the key carry cubic units for volume and square units for surface area, so check that the student's units match.

Worked example: a prism 8 cm long, 5 cm wide, 3 cm high

Volume

  1. Multiply the three edges: 8 × 5 = 40.
  2. 40 × 3 = 120.
  3. Volume = 120 cm³.

Surface area

  1. A prism has three different pairs of faces. Bottom and top: 8 × 5 = 40 each.
  2. Front and back: 8 × 3 = 24 each.
  3. Left and right: 5 × 3 = 15 each.
  4. Add one of each pair: 40 + 24 + 15 = 79.
  5. Double it, since every face has a twin: 79 × 2 = 158.
  6. Surface area = 158 cm².

For a cube with edge 4 cm, volume is 4 × 4 × 4 = 64 cm³. Each face is 16 cm² and there are six, so the surface area is 96 cm².

Common errors on the key

  • Adding instead of multiplying for volume. Getting 16 for the prism above. The key's number is much larger.
  • Counting three faces, not six. The student's surface area is exactly half the key's, 79 instead of 158.
  • Mixing up units. 120 cm² instead of 120 cm³.
  • Using the wrong pair of edges. Multiplying 8 × 5 for the front face. Have students tick off each pair of faces on the picture as they go.

Helping students see it

Build a prism from centimeter cubes or stacked sticky notes, or use a cereal box and a ruler. Peel the box open flat to show the six rectangles and count them. Students who have seen a net rarely forget that surface area is a sum of flat pieces. For triangular faces, such as a prism's end, the earlier skill of finding the area of a triangle is the next building block.

Sources

  1. Common Core State Standards: Grade 6 Geometry (6.G.A.2, volume of a right rectangular prism; 6.G.A.4, surface area using nets) thecorestandards.org
  2. Common Core State Standards: Grade 5 Measurement and Data (5.MD.C.5, relate volume to multiplication and addition) thecorestandards.org