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8th grade Square-based pyramids: volume and surface area worksheet

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Square-based pyramids: volume and surface area

Grade 8 Math Worksheet

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  1. Pia's model pyramid has base edges of 9 cm, a height of 6 cm and a slant height of 7.5 cm. What is its volume, in cubic cm? Do not round.

  2. Tala's big paper pyramid has base edges of 21 cm, a height of 14 cm and a slant height of 17.5 cm. What is its volume, in cubic cm? Do not round.

  3. Zee's pyramid sculpture has base edges of 7.2 meters, a height of 4.8 meters and a slant height of 6 meters. What is its volume, in cubic meters? Do not round.

  4. Ari's pyramid model has base edges of 7 cm, a slant height of 12.5 cm and a height of 12 cm. What is its surface area, in square cm?

  5. Bo's castle roof has base edges of 8 inches, a slant height of 8.5 inches and a height of 7.5 inches. What is its surface area, in square inches?

  6. Esme's paper pyramid has base edges of 20 cm, a slant height of 14.5 cm and a height of 10.5 cm. What is its surface area, in square cm?

  7. Jun's pyramid sculpture has base edges of 1.4 meters, a slant height of 2.5 meters and a height of 2.4 meters. What is its surface area, in square meters?

  9. Kira wants the volume of a square pyramid model. Which length goes with the base area to find it?

    • The height, straight down from the tip to the middle of the base
    • The slant height, from the tip down the middle of a face of the pyramid
    • The edge from the tip down to a corner of the base

  10. Luz wants to know how much paper covers the four triangles of a square pyramid. Which length is each triangle's height?

    Use the picture in question 8.

    • The edge from the tip down to a corner of the base
    • The height, straight down from the tip to the middle of the base
    • The slant height, from the tip down the middle of a face

  11. Noah is painting the faces of a square pyramid model. Which length is the height of each triangle face?

    Use the picture in question 8.

    • The height, straight down from the tip to the middle of the base
    • The slant height, from the tip down the middle of a face
    • The edge from the tip down to a corner of the base
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8th grade Square-based pyramids: volume and surface area worksheet – printable
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About this worksheet

Square-based pyramids: volume and surface area. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find a square pyramid's volume: one third of the prism with the same base and height.
  • I can find its surface area from its net: the square base and four triangles, each base × slant height ÷ 2.
  • I can tell the height (inside, straight down to the middle of the base) from the slant height (down the middle of a face), and find one from the other.

Standard: state-only (CCSS K–8 has no pyramid volume; surface area from nets is 6.G.A.4)

Words to know

square pyramid: A solid with a square base and four triangle faces meeting at a tip.

height: Straight down from the tip to the middle of the base, inside the pyramid.

slant height: From the tip down the middle of a face to the middle of a base edge.

net: The pyramid unfolded flat: the square and its four triangles.

surface area: The total area of all five faces.

volume: How much the pyramid holds, in cubic units.

Common mistakes

Your child gave the volume of the whole prism. A pyramid with the same base and height holds one third of it: three pyramids of sand fill the prism.

Your child took half instead of one third. A pyramid holds one third of the prism with the same base and height: it takes three pours to fill the prism.

Your child multiplied by three instead of dividing. The pyramid is the smaller solid: it holds one third of its prism.

Questions parents ask

What is the most common mistake with square-based pyramids: volume and surface area?

Your child gave the volume of the whole prism. A pyramid with the same base and height holds one third of it: three pyramids of sand fill the prism.

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

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