homework and practice 10 3 volume of prisms

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Volume of a Prism Worksheets

This extensive compilation of printable volume of prisms worksheets enables 7th grade, 8th grade, and high school students to find the volume of triangular, rectangular, trapezoidal and polygonal prisms. Featured here are innumerable exercises to practice finding the volume of prisms using dimensions of varying base faces expressed as decimals and integers. The worksheets offer problems presented as 3D shapes and word format with easy and moderate levels classified based on the range of numbers used. Access some of them for free!

Find the Volume of Prisms using Base Area | Integers

The area of the base face of each prism and a dimension are expressed as integers. Multiply the two to compute the volume of the triangular and rectangular prisms featured in these worksheets.

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Find the Volume of Prisms using Base Area | Decimals

Intensify the practice in calculating the volume of prisms efficiently and accurately using decimal measures. Determine the volume of six 3D shapes and two-word format problems in each printable worksheet for grade 7.

Volume of Prisms | Bases - Trapezoid and Parallelogram

Incorporate these pdf worksheets on volume of prisms encompassing trapezoidal and parallelogram bases offering an easy level for beginners with dimensions ≤ 20 and a moderate level with 2-digit dimensions.

Volume of Prisms | Bases -Trapezoid and Parallelogram | Decimals

Work out each problem by finding the area of the trapezoidal or parallelogram base faces. To do this, simply plug the known values expressed as decimals into the formula and determine the volume.

Volume of Polygonal Prisms | Level 1

Get a hands-on experience in finding the volume of regular prisms using the side length, apothem and the height given. The polygons featured here range from three-sided to six-sided figures.

Find the Volume of Polygonal Prisms | Level 2

Raise the bar with this set of volume of polygonal prism worksheets. Employ the height and the given perimeter or side length to find the apothem and then determine the volume of each prism.

Volume of Prisms | Revision - Integers | Level 1

Perfect as a review exercise, these printable worksheets present prisms with triangular or quadrilateral bases with two levels of difficulty. Begin with the easy level, then move on to the moderate level.

Volume of Prisms | Mixed Review - Decimals | Level 1

Find the volume of each of the eight prisms that are a mix of triangular and quadrilateral base faces with measures denoted as decimals. Direct students of grade 8 and high school to apply relevant formulas to solve for the volume.

Volume of Prisms | Mixed Review | Level 2

Intensify your practice and level up with this cluster of pdf volume of mixed prisms worksheets involving triangular, quadrilateral and polygonal bases and dimensions depicted as decimals and integers.

Find the Missing Dimensions

Review the concept of finding the volume with prisms whose bases are either triangles, squares, rectangles or parallelograms. Use the volume and the dimension provided to solve for the unknown measure.

Volume of Rectangular Prisms

Get your brains active with this bundle of rectangular prisms pdf worksheets. Compute the volume of rectangular prisms and crosscheck with the answer keys for an instant validation.

(33 Worksheets)

Volume of Triangular Prisms

Learn to apply the area of the cross-section and the known dimensions in the formula to find the volume of each triangular prism. Practice finding the missing dimensions as well.

(24 Worksheets)

Related Worksheets

» Volume of Composite Shapes

» Volume by Counting Cubes

» Volume of Cubes

» Volume of Cylinders

» Volume of Mixed Shapes

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9.10: Surface Area and Volume of Prisms

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3-D figures with 2 congruent bases in parallel planes and rectangles for their other faces.

A prism is a 3-dimensional figure with 2 congruent bases, in parallel planes, in which the other faces are rectangles.

The non-base faces are l ateral faces . The edges between the lateral faces are lateral edges .

This particular example is a pentagonal prism because its base is a pentagon. Prisms are named by the shape of their base. Prisms are classified as either right prisms (prisms where all the lateral faces are perpendicular to the bases) or oblique prisms (prisms that lean to one side, whose base is a parallelogram rather than a rectangle, and whose height is perpendicular to the base's plane), as shown below.

Surface Area

To find the surface area of a prism, find the sum of the areas of its faces. The lateral area is the sum of the areas of the lateral faces. The basic unit of area is the square unit.

\(Surface Area=B_{1}+B_{2}+L_{1}+L_{2}+L_{3}\)

\(Lateral Area=L_{1}+L_{2}+L_{3}\)

To find the volume of any solid you must figure out how much space it occupies. The basic unit of volume is the cubic unit.

For prisms in particular, to find the volume you must find the area of the base and multiply it by the height.

Volume of a Prism: \(V=B\cdot h\), where \(B= area\: of\: base\).

If an oblique prism and a right prism have the same base area and height, then they will have the same volume. This is due to Cavalieri’s Principle , which states that if two solids have the same height and the same cross-sectional area at every level, then they will have the same volume.

What if you were given a solid three-dimensional figure with two congruent bases in which the other faces were rectangles? How could you determine how much two-dimensional and three-dimensional space that figure occupies?

Example \(\PageIndex{1}\)

The total surface area of the triangular prism is \(540\text{ units}^{2}\). What is \(x\)?

The total surface area is equal to:

\(A_{2\: triangles}+A_{3\: rectangles}=540\)

The hypotenuse of the triangle bases is 13, \(5^{2}+12^{2}\). Let’s fill in what we know.

\(\begin{aligned} A_{2\: triangles}=2(\dfrac{1}{2}\cdot 5\cdot 12)=60 \\ A_{3\: rectangles}&=5x+12x+13x=30x \\ 60+30x &=540 \\ 30x&=480 \\ x&=16\text{ units }\qquad \text{ The height is 16 units.}\end{aligned}\)

Example \(\PageIndex{2}\)

Find the volume of the right rectangular prism below.

The area of the base is \((5)(4)=20\) and the height is 3. So the total volume is \((20)(3)=60\text{ unit}^{3}\)

Example \(\PageIndex{3}\)

Find the surface area of the prism below.

To solve, draw the net of the prism so that we can make sure we find the area of ALL faces.

Using the net, we have:

\(\begin{aligned} SA_{prism}&=2(4)(10)+2(10)(17)+2(17)(4)\\ &=80+340+136 \\ &=556 \text{ cm}^{2}\end{aligned}\)

Example \(\PageIndex{4}\)

This is a right triangular prism. To find the surface area, we need to find the length of the hypotenuse of the base because it is the width of one of the lateral faces. We can use the Pythagorean Theorem to find this length.

\(\begin{aligned} 7^{2}+24^{2}&=c^{2} \\ 49+576&=c^{2} \\ 625&=c^{2} \qquad c=25\end{aligned}\)

Looking at the net, the surface area is:

\(\begin{aligned} SA&=28(7)+28(24)+28(25)+2(\dfrac{1}{2}\cdot 7\cdot 24) \\ SA&=196+672+700+168=1736 units^{2}\end{aligned}\)

Example \(\PageIndex{5}\)

You have a small, triangular prism-shaped tent. How much volume does it have once it is set up?

First, we need to find the area of the base.

\(\begin{aligned} B&=\dfrac{1}{2}(3)(4)=6 \text{ ft}^{2} \\ V&=Bh=6(7)=42 \text{ ft}^{3}\end{aligned}\)

Even though the height in this problem does not look like a “height,” it is because it is the perpendicular segment connecting the two bases.

• Draw the net of this prism.
• Find the area of the bases.
• Find the area of lateral faces, or the lateral surface area.
• Find the total surface area of the prism.
• How many one-inch cubes can fit into a box that is 8 inches wide, 10 inches long, and 12 inches tall? Is this the same as the volume of the box?
• A cereal box in 2 inches wide, 10 inches long and 14 inches tall. How much cereal does the box hold?
• A can of soda is 4 inches tall and has a diameter of 2 inches. How much soda does the can hold? Round your answer to the nearest hundredth.
• A cube holds \(216\text{ in}^{3}\). What is the length of each edge?
• A cube has sides that are 8 inches. What is the volume?

Use the right triangular prism to answer questions 11-15.

• Find the volume of the prism.
• What shape are the bases of this prism? What are their areas?
• What are the dimensions of each of the lateral faces? What are their areas?
• Find the lateral surface area of the prism.
• Describe the difference between lateral surface area and total surface area.

• What is the volume and surface area of one die?
• What is the volume and surface area of both dice?

Find the volume of the following solids. Round your answers to the nearest hundredth.

Find the value of \(x\), given the surface area.

Review (Answers)

To see the Review answers, open this PDF file and look for section 11.3.

Additional Resources

Interactive Element

Video: Prisms Principles - Basic

Activities: Prisms Discussion Questions

Study Aids: Prisms and Cylinders Study Guide

Practice: Surface Area and Volume of Prism

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Course: 5th grade   >   Unit 11

• Measuring volume as area times length
• Volume as area of base times height
• Volume of a rectangular prism

Volume of rectangular prisms

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Chapter 10, Lesson 6: Volume of Rectangular Prisms

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Volume of prisms practice

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Decompose Rectangular Prisms

Related Topics: Lesson Plans and Worksheets for Grade 5 Lesson Plans and Worksheets for all Grades More Lessons for Grade 5 Common Core For Grade 5

Videos, examples, solutions, and lessons to help Grade 5 students learn how to compose and decompose right rectangular prisms using layers.

Worksheets for Grade 5

Common Core Standards: 5.MD.3, 5.MD.4

Lesson 3 Concept Development

Lesson 3 Problem Set

• Use the prisms to find the volume.
• Build the rectangular prism pictured below to the left with your cubes, if necessary.
• Decompose it into layers in three different ways, and show your thinking on the blank prisms.
• Complete the missing information in the table.
• Josh and Jonah were finding the volume of the prism to the right. The boys agree that 4 layers can be added together to find the volume. Josh says that he can see on the end of the prism that each layer will have 16 cubes in it. Jonah says that each layer has 24 cubes in it. Who is right? Explain how you know using words, numbers, and/or pictures.

Lesson 3 Homework This video shows how to find the volume of rectangular prisms using a method of decomposing in layers.

• The rectangular prisms pictured below were constructed with 1-cm cubes
• Decompose each prism into layers in three different ways, and show your thinking on the blank prisms.
• Complete each table
• Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters. Chelsea wants to add eight layers and Stephen says they only need to add four layers. Their teacher tells them they are both correct. Explain how this is possible.

Lesson 3 Homework 4. Imagine the rectangular prism below is 4 meters long, 3 meters tall, and 2 meters wide. Draw horizontal lines to show how the prism could be decomposed into layers that are 1 meter in height. It has _____ layers from left to right. Each layer contains ______ cubic units. The volume of this prism is __________.

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