# Volume Worksheets

## Volume Worksheets for Math

I have collected a series of links for volume worksheets for your mathematics class. The worksheets start with the simplest level of counting cubes and increase in complexity through rectangular prisms to cylinders, cones and spheres. There is also a section on mixed solids to provide for revision at the end of the unit.

In each section I am including the formulas for calculating the volumes of the various three-dimensional solids. Near the bottom of this article, I am also sharing a few hands-on activities for younger students to add variety to your lessons.

3D shapes picture modified from clker.

## Simple Volume Worksheets - Counting boxes

Cube picture based on this picture from clker

www.superteacherworksheets.com

There are is a free worksheet under the heading Volume Cubes where you count the cubes to find the volume - includes answers.

The printable sheets under third grade (grid method) and fourth grade (volume - pictorial) are all about calculating the volume of 3D shapes by counting cubes.

Links checked Nov 2013

## Definition of Terms

A prism is a solid with two bases of the same size and shape. These bases may be square, rectangular, triangular, or another polygon. The other faces of the prism will be squares or rectangles. Cross sections of a prism cut parallel to the base will all be the same size and shape as the base.

A pyramid has only one base which can be a square, triangle or other polygon. The other faces of the pyramid will be triangles which all meet at a common vertex (the top). Cross sections of pyramid cut parallel to the base will all be the same shape as the base but will also be a different size.

A cone has a circular base and one vertex.

A sphere is a solid where all points on the surface are the same distance from the center (like a ball)

## Cubes and Rectangular Prisms / Cuboids

Cuboid

V = w * L * h

where w = width of the rectangular base

L = length of the rectangular base

h = height of prism

www.superteacherworksheets.com

Scroll down to the Foldable cube and just for fun, make a cube from this printable pattern. After the students have completed their cubes, they could measure the sides and calculate the volume.

At the top of this page, you'll find 3 rectangular prism and 3 cube worksheets.

Find the missing values for these rectangular prisms

6 rectangular prisms - metric

6 rectangular prisms - metric

Links checked Dec 2013

## Triangular Prisms

Triangular prism

V = Â½ b * h * L

where b = base of triangle

h = height of triangle

L = length of prism

Scroll down to Volume of Triangular Prism for two triangular prism worksheets

Online activity investigating right triangular prisms + answers

Online activity investigating triangular prisms + answers

Links checked Jan 2014

## Cylindrical Prism / Cylinders

Cylinder

V = π * r 2 * h

where π = pi = 3.14159......

r = radius

h = height

A cylinder activity sheet where the students make the cylinders from paper

Scroll down to the Volume of Cylindrical Prism: heading for 3 cylinder worksheets (with answers)

Scroll down to Clay Cylinder for a pdf document with instructions to make a mug from clay, making measurements and calculations

Online activity investigating cylinders + answers

Links checked Oct 2013

## Square and Rectangular Pyramids

Rectangular pyramid

V = 1/3 * L * w * h

where L = length of rectangle

w = width of rectangle

h = height of pyramid

Just for fun, make a pyramid from this printable page. After the students have completed their pyramids, they could measure them and calculate the volume. Measuring the height could be a special challenge!

Search for Rectangular Pyramid and Square Pyramid for 4 printable sheets - includes answers

Online puzzle investigating rectangular pyramids + answers

Links checked Oct 2013

## Triangular Pyramids

Triangular pyramid

V = 1/6 * b * h * H

where b = base of the base triangle

h = height of the base triangle

H = height of pyramid

Just for fun, make a pyramid from these foldable tetrahedrons in three different sizes. After the students have completed their pyramids, they could measure them and calculate the volume. Measuring the height could be a special challenge!

Search for Triangular Pyramid for 2 worksheets - includes answers

Online puzzle investigating triangular pyramids + answers

Links checked Apr 2014

## Cones

Cone

V = 1/3 * π * r 2 * h

where π = pi = 3.14159...

r = radius of the circular base

h = height of the cone

Scroll down to the Volume of Cone heading for 3 cone worksheets - includes answers

Online activity investigating cones + answers

You can practice on this interactive page, changing the height or radius of the cone by clicking and dragging the dot markers. You can also click on questions, more practice, and spreadsheet on the right hand side of the page for more cone problems.

Links checked July 2012

## Spheres

Sphere

V = 4/3 * π * r 3

where π = pi = 3.14159......

r = radius

Scroll down to the Volume of Sphere heading for 3 sphere printable sheets - includes answers

Online puzzle investigating spheres + answers

Under the heading Surface Area and Volume you'll find a worksheet on spheres. The first half of this sheet is for determining surface area of spheres and the second half is determining volume of spheres. Answers given.

Links checked July 2012

## Mixed Solids

Create a randomly produced sheet of word problemst. Untick the box next to area of a circle etc and just leave the box next to Volume of a cylinder, rectangular box and/or sphere ticked. Then click on the button, Create Printable Worksheet. Answer sheet also available.

Scroll to the bottom of this page for:

- Prisms and cylinders (with diagrams)

- Cones, pyramids and sphere (with diagrams)

- Prisms, cylinders, cones, pyramids, and spheres (no diagrams) - to the nearest tenth

Scroll to the bottom of this page to find a worksheet on Volume of a prism (a variety of prisms).

Under the heading Surface Area and Volume you'll find a worksheet for finding the volume of prisms and cylinders (includes a pentagonal prism and a hexagonal prism + word problems) and one for finding the volume of cones and pyramids (includes pentagonal pyramids and hexagonal pyramids + word problems). Answers given.

There are three fun activities here:

Worksheet 3 Printable - What will fit? Rectangular prism, cylinder and square pyramid

Extension bonus - Turn up the volume. Cuboids and pyramids

Extension take home - The perfect fit. Rectangular prisms and cylinders

Scroll down to View quiz for some volume and surface area word problems for grades 6-8.

Links checked Jul 2012

## Hands-on Activities for Younger Students

- Students build structures (eg a house, bridge, a tower) using identical sized boxes, Lego pieces, or blocks. Count the number or blocks or boxes used and compare the size of the structures by eye.
- Build different structures using the same number of identical sized boxes or blocks. Compare their sizes by eye.
- Measure the capacity of a variety of containers by filling them with sand, rice, or water from a smaller container (eg fill a bucket using a cup or a cap using a thimble). Students could estimate the capacity first.
- Estimate the capacity of various containers to the nearest pint / gallon / quart / litre etc. Check your estimates by actually filling the containers using a known measure.
- Make a set of nesting prisms from card.
- Draw a 2 inch (5cm) square on a piece of paper. Take a ball of play dough, sit it on your square, and using two CD boxes (or other flat surfaces) squeeze the sides of the play dough until it fits the square. Keep doing this with all the sides until you have made a cube. You may need to add more play dough or take some away to get your cube. Now you have a cube measuring 2in x 2in x 2in = 8 cubic inches (or 5cm x 5cm x 5cm = 125 cubic cm). Now make different shapes and creations with this play dough, not adding any, or taking any away. All of your creations will have a volume of 8 cubic inches (125 cubic centimetres).

## Manipulatives for Examining and Exploring Capacity

This measuring / play set has a rectangular prism, a square prism, a cube, a small triangular prism, a large triangular prism, a hexagonal prism, a sphere, a hemisphere, a cylinder,a cone, a square pyramid, and a triangular pyramid. All these containers are translucent and have lids so that they can be used for measuring solids or liquids. This is a great set for estimating and comparing volumes. They can also be used for filling larger containers.

## More Math Printables

Area Worksheets On this page you'll find area worksheets for rectangles, triangles, parallelograms, trapezoids, circles, and more shapes.

Printable Math Games I have collected a series of printable math games for teachers and parents to print out and play with their children. Many of these games are multi-player, allowing them to be played with 2 or more students but some of them are single-player - for 1 student to play on his own.

Geometric Coloring Pages Now here's something really fun! Whether you want geometric coloring pages for educational purposes or just for fun, you're bound to find something to suit you here. Color square patterns, circular patterns, tessellations, kaleidoscopes, celtic knots, and much more.

Dot to Dot Printable PagesDozens of dot to dot printables sorted into difficulty levels, ranging from very easy to extreme. There are also puzzles for skip counting and also alphabet dot to dot.

## Your Comments Welcome - Thanks for reading!

Seems like you covered most of them. Wonderful!

Fantastic!

That's a great and helpful collection!

i might include the Rubik's cube as a tangible way of understanding the cube! cheers

Nice lens! it reminds me time at school :) (and I still remember all the formulas)

Great lens! I'm a middle school teacher and I could see how some of these would really help. Thanks!

I never did do too well on geometry, these worksheets make it easier to relearn.

great info source

I don't have a suggestion--I just know that my daughter taught math and she would have loved this. Great job.

Can't suggest anything new, but you bet I am going to check these! Thanks for your list!

Yay! Nice collection of volume formulas and worksheet.

Dosent rally help that much=(

Very nice, thanks a lot.. also this might help Cylinder Volume

I love the way you laid out the information; this is very useful.

This is a great resource for maths students of ALL ages!

Excellent page and so much help for struggling students. I always loved math but for whatever reason, geometry was just a struggle for me. I know you'll help others like me with this page. Happy Pi Day!

This page will be really useful for my daughter when she starts studying volume soon.

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