Grade 7 · Math

7th grade Volume of prisms and pyramids worksheet

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Volume of prisms and pyramids

Grade 7 Math Worksheet - Building Confidence

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Jun's cheese wedge is a prism 5 cm long. Its end is half of a rectangle 8 cm by 6 cm. The mice have heard about it. What is its volume in cubic cm?
Pia's treasure box is a prism 2 in long. Its end is a trapezoid: parallel sides 4.5 and 1.5 in, height 4 in. It guards one shiny button. What is its volume in cubic inches?
Ren's toy cart basket is a prism 3 in long. Its end is a trapezoid: parallel sides 5 and 2 in, height 4 in. It rolls squeakily. What is its volume in cubic inches?
Tala's model recycling bin is a prism 3.5 in long. Its end is a trapezoid: parallel sides 6 and 3 in, height 4 in. It is tidy. What is its volume in cubic inches?
Bo's playhouse roof has a base of 16 square cm and is 9 cm tall. Three of these pyramids fill the matching prism. A chimney peeks out. What is its volume in cubic cm?
Esme's cheese wedge is a prism. Its end is half of a rectangle 9 cm by 12 cm, with slanted side 15 cm. Mice approve. What is its end's area (one layer) in square cm?
Kira's toy ramp is a prism. Its end is half of a rectangle 0.9 cm by 1.2 cm, with slanted side 1.5 cm. Wheels ready. What is its end's area (one layer) in square cm?
Luz's craft box is a prism. Its end is a trapezoid: parallel sides 8 and 5 in, height 4 in. Glitter everywhere. What is its end's area (one layer) in square inches?
Milo's treasure box is a prism. Its end is a trapezoid: parallel sides 4 and 1 in, height 4 in. Shiny inside. What is its end's area (one layer) in square inches?
Noah's model recycling bin is a prism. Its end is a trapezoid: parallel sides 7 and 4 in, height 4 in. It is tidy. What is its end's area (one layer) in square inches?

7th grade Volume of prisms and pyramids worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Volume of prisms and pyramids. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the volume of a prism by finding the area of its end (one layer) and stacking it along the length, even when the end is a triangle or a trapezoid.
I can find the volume of a pyramid as one third of the prism with the same base and height, and work back to a missing length or height.
I can say how the volume changes when one edge gets longer or shorter, and add the parts of a solid made of two shapes.

Standard: 7.G.B.6 (prisms and shapes built from cubes and prisms; CCSS K–8 has no pyramid volume)

Words to know

prism: A solid with two matching ends and flat sides. Its layers are all the same shape.

pyramid: A solid with one flat base and flat faces that meet at a point (the tip).

base (end): The flat shape that is stacked, layer by layer, to make a prism.

height of a pyramid: The straight-up distance from the base to the tip.

face height (slant): How far it is along a face from the base edge to the tip. It leans, so it is longer than the height.

volume: How much space is inside a solid, counted in cubes.

cubic centimeter (inch, foot): The volume of a cube 1 centimeter (inch, foot) on every edge.

Common mistakes

Your child added the three edges instead of multiplying. Fill a small box with cubes together: count one floor layer, then count how many layers stack up.

Your child found the area of the floor or the end and stopped before stacking it.

Your child used the rectangle around a triangle or trapezoid end and forgot that the end is only half of it. Cut two paper copies of the end shape and fit them into a rectangle together.

What to say

Ask: how many layers like that fit in the height or the length?

Questions parents ask

What is the most common mistake with volume of prisms and pyramids?

Your child added the three edges instead of multiplying. Fill a small box with cubes together: count one floor layer, then count how many layers stack up.

Are these 7th 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 7 math

See all grade 7 math

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