Grade 7 · Math

7th grade Volume of prisms and pyramids worksheet

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Volume of prisms and pyramids

Grade 7 Math Worksheet

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Pia's cheese block is a prism 5 cm long. Its end is a right triangle: base 12, height 9, slanted side 15 cm. It has lots of holes. What is its volume in cubic cm?
Tala's paper tent is a prism 8 in long. Its end is a triangle: base 9, height 6, two slanted sides of 7.5 in. Tape holds it up. What is its volume in cubic inches?
Zee's recycling bin is a prism 10 in long. Its end is a trapezoid: parallel sides 15 and 10, height 12, slanted side 13 in. It is ready. What is its volume in cubic inches?
Bo's storage box is a prism 6 in long. Its end is a trapezoid: parallel sides 9.5 and 6.5, height 4, slanted side 5 in. Socks hide here. What is its volume in cubic inches?
Jun's playhouse roof has a base of 4.5 in by 4 in and a height of 5 in. A chimney peeks out. What is its volume in cubic inches?
6.
Milo's storage box is a prism 4 in long. Its end is a trapezoid: parallel sides 7 and 2.5, height 6, slanted side 7.5 in. Socks hide here. Which expression gives its volume?
- (7 + 2.5) × 6 × 4
- (7 + 2.5) × 6 ÷ 2 × 4
- (7 + 2.5) × 7.5 ÷ 2 × 4
- 7 × 6 × 4
7.
Noah's toy cart basket is a prism 3 in long. Its end is a trapezoid: parallel sides 5 and 3.2, height 2.4, slanted side 3 in. It squeaks. Which expression gives its volume?
- 5 × 2.4 × 3
- (5 + 3.2) × 3 ÷ 2 × 3
- (5 + 3.2) × 2.4 ÷ 2 × 3
- (5 + 3.2) × 2.4 × 3
Ren's storage box holds 24 cubic inches. Ren makes its height 3 times as long. It is extra roomy now. What is its new volume in cubic inches?
Ren's cheese block is a prism. Its end is a triangle: base 18, height 24, slanted side 30 cm. Lots of holes. What is its end's area (one layer) in square cm?
Zee's recycling bin is a prism. Its end is a trapezoid: parallel sides 15 and 10, height 12, slanted side 13 in. Always ready. 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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