Grade 8 · Math

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 - Building Confidence

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Pia makes a model pyramid for history class. A square prism with the same base and height holds 300 cubic cm. What is the pyramid's volume, in cubic cm?
Ren makes a square pyramid roof for a model castle tower. A square prism with the same base and height holds 225 cubic inches. What is the pyramid's volume, in cubic inches?
Use the picture in question 1.
Zee makes a glass pyramid paperweight. A square prism with the same base and height holds 432 cubic cm. What is the pyramid's volume, in cubic cm?
Use the picture in question 1.
Bo unfolds a model castle roof: a square base of 100 square inches and four triangles of 65 square inches each. What is its surface area, in square inches?
Esme unfolds a small pyramid model: a square base of 36 square cm and four triangles of 39 square cm each. What is its surface area, in square cm?
Jun unfolds a pyramid gift box made of card: a square base of 144 square cm and four triangles of 102 square cm each. What is its surface area, in square cm?
Kira measures a pyramid sculpture in the park. Its height, 2.1 meters, and half its base, 2 meters, are the legs of a right triangle inside. How long is the slant height, in meters?
Luz measures a tall castle tower roof. Its height, 30 cm, and half its base, 12.5 cm, are the legs of a right triangle inside. How long is the slant height, in cm?
Milo measures a pyramid model for the school hall. Its height, 3 feet, and half its base, 1.25 feet, are the legs of a right triangle inside. How long is the slant height, in feet?
Noah measures a tall paper pyramid. Its height, 17.5 cm, and half its base, 6 cm, are the legs of a right triangle inside. How long is the slant height, in cm?

8th grade Square-based pyramids: volume and surface area worksheet – printable — Print: 1 2 3 4 5 6

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

See all grade 8 math

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