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- Mixed Prisms

## 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.

- Download the set

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

## Volume of a Prism Practice Questions

Click here for questions, click here for answers, gcse revision cards.

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## Volume of prisms

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

15 May 2019

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TWO FULL LESSONS on finding the volume of prisms.

Contents of download:

- Higher ability full lesson (5.2.1h) on volume of prisms (could be taught over one or two lessons depending on previous knowledge).
- Lower ability full lesson (5.2.1f) on volume of prisms (to be taught over one or two lessons depending on previous knowledge). Ex4 and Ex5 are a suggested starting point for lesson two .
- Examples (to go with PowerPoint)
- Worksheets with solutions (printed and displayed on PowerPoint).

We are learning about: The volume of a prism We are learning to: Calculate the volume of a prism.

Differentiated objectives:

- Developing learners will be able to calculate the volume of a prism.
- Secure learners will be able to find the missing length of a prism given its volume and cross-section.
- Excelling learners will be able to solve unfamiliar problems using their knowledge of calculating the volume of a prism.

Main: Walkthrough examples followed by practice questions on worksheets. All solutions given on PPT and in worksheet format.

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Lesson 4 Homework Practice Volume of Prisms Find the volume of each prism. Round to the nearest tenth if necessary. 1. 10 in. 5 in. 7 in. 2. 6 m 8 m 12 m 3. 4.2 ft 2 ft 3.5 ft 4. 1.1 mm 2.6 mm 1.5 mm 5. ... Sample answer: 7 × 4 × 3 or Sample answer: (0.5 × 5 × 6) × 6 84 yd3 or 90 m3

Find the volume of each prism. Round to the nearest tenth if necessary. 1. 3 cm 7 cm 3 cm 2. 6 in. 10 in. 5 in. 3. 4 m 4 m 6 m 4. 3 mm 5 mm 12 mm 5. 7 in. 2.8 in. 9.5 in. 6. 7.2 m 3 m 9 m 7. 4 ft 4 ft 3 4 2 ft 1 2 8. 15 in. 9.6 in. 4.8 in. 9. 4.5 cm 1.2 cm 1.5 cm Lesson 4 Skills Practice Volume of Prisms 63 cm3 300 in3 96 m3 90 mm3 186.2 in3 97 ...

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 11 feet by 3 inches for a patio if the concrete costs $63.00 per cubic yard? $70.58. The volume of a cylinder is 980𝜋 in^3. The height of the cylinder is 20 in. What is the radius of the cylinder? 7 in. Find the volume of the cylinder in terms of 𝜋. (https ...

Lesson 4 Homework Practice Volume of Prisms Find the volume of each prism. Round to the nearest tenth if necessary. 1. ... MAIL The United States Post Office has two different priority mail flat rate boxes. Which box has the greater volume? Justify your answer. Box 1: in. × in. × 11 in. Box 2: in. × in. × in. 6.1 m 5.9 m 4.8 m yd ...

Lesson 4 Extra Practice . Volume of Prisms . Find the volume of each prism. Round to the nearest tenth if necessary. 1. 24 ft. 3: 2. 2 yd. 3: 3. 150 mm. 3: 4. 34 cm. 3: 5. 432 in. 3: 6. 962.5 m. 3: 7. 240 mm. 3: 8. 660 yd. 3: Course 2 • Chapter 8 Measure Figures . 15 yd 8Yd 11 yd 17 yd 12 mm 5 mm 6 in. 18 in. 85 cm 2 cm \ 14 mm 3 mm 4 mm ...

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 ...

Lesson 4 Problem-Solving Practice Volume of Prisms 1. PACKAGING A cereal box has a length of 8 inches, a width of 1 −3 inches, 4 and a height of 12 −1 inches. What is 8 the volume of the cereal box? 2. FOOD STORAGE Nara wants to determine how much ice it will take to fill her cooler that is in the shape of a rectangular prism. If the cooler

Prisms, pyramids, cylinders cones surface area worksheets. Lesson 2 homework practice percents and fractions answers. 20 ft 24. group practice . Volume and surface area of triangular prisms a . Lesson 9 homework 5/3 bank locations. 4 pages take home practice test. Lesson 3 homework practice angles of triangles total.

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 ⋅ h V = B ⋅ h, where B = area ofbase B = a r e a o f b a s e. Figure 9.10.4 9.10. 4. If an oblique prism and a right prism have the same base area and height, then they will have the same volume.

Volume of rectangular prisms. Google Classroom. What is the volume of the rectangular prism? 7 cm 4 cm 5 cm. cm 3. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone ...

The volume is 22 cubic inches. Lesson Tutorials. Section 7.1 Volumes of Prisms 301 3 in. 4 in. 4 in. Bag A Bag B 4 in. h h Find the volume of the prism. Exercises 4 -12 1. 4 ft 4 ft 5 ft 2. 12 m 9 m 5 m EXAMPLE 3 Real-Life Application A movie theater designs two bags to hold 96 cubic inches of popcorn. ... Help with Homework 1 2 Gym Locker ...

The Corbettmaths Practice Questions on the Volume of a Prism. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths ... Click here for Answers . Practice Questions. Previous: Volume of a Cuboid/Cube Practice Questions. Next: Volume of a Cylinder Practice Questions. GCSE Revision Cards. 5-a ...

As a guest, you only have read-only access to our books, tests and other practice materials. As a registered member you can: View all solutions for free; Request more in-depth explanations for free; Ask our tutors any math-related question for free; Email your homework to your parent or tutor for free

Find the volume of each prism. Round to the nearest tenth if necessary. 1. 3 cm 7 cm 3 cm 2. 6 in. 10 in. 5 in. 3. 4 m 4 m 6 m 4. 3 mm 5 mm 12 mm 5. 7 in. 2.8 in. 9.5 in. 6. 7.2 m 3 m 9 m 7. 4 ft 4 ft 3 4 2 ft 1 2 8. 15 in. 9.6 in. 4.8 in. 9. 4.5 cm 1.2 cm 1.5 cm Lesson 4 Skills Practice Volume of Prisms

378 Chapter 8 Surface Area and Volume Help with Homework Find the volume of the prism. 1 4. 2 3 in. 3 5 in. 3 4 in. 5. 1 2 cm 3 2 cm 7 4 cm 6. 2 5 ft 2 5 ft 2 5 ft 7. 3 4 m 2 m 5 8 m 8. 5 6 cm 1 cm 2 3 2 cm 1 4 9. 3 m 1 8 2 m 4 5 1 m 3 7 Write and solve an equation to ﬁ nd the missing dimension of the prism. 10. Volume = 1620 cm3 11. Volume ...

Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor Self-Check Quizzes. Common Core State Standards Supplement, SE Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Study to Go Online Calculators. Mathematics. Home > Chapter 12 > Lesson 4. Geometry. Chapter 12, Lesson 4: Volumes of ...

TWO FULL LESSONS on finding the volume of prisms.. Contents of download: Higher ability full lesson (5.2.1h) on volume of prisms (could be taught over one or two lessons depending on previous knowledge). Lower ability full lesson (5.2.1f) on volume of prisms (to be taught over one or two lessons depending on previous knowledge).Ex4 and Ex5 are a suggested starting point for lesson two.

Lesson 4 Homework Practice Surface Area of Triangular Prisms Find the surface area of each triangular prism. Round to the nearest tenth if necessary. 1. 6 km 14 km 6 km 6 km 5.2 km 2. 2.6 ft 6.5 ft 3 ft 4 ft 3. 17 in. 12 in. 23.2 in. 24 in. 16.4 in. 4. 6.5 mm 2.5 mm 8 mm 6 mm 5. One foam block on the playground at Teeny Tots Preschool is a ...

1800m³. What is the volume of a triangular prism with length 14m, width 7m and height 20m? 980m³. What is the volume of a triangular prism with length 3m, width 4m and height 6m? 48m³. What is the volume of a cylinder with radius 5m and height 12m? 300πm³. What is the volume of a cylinder with radius 10m and height 8m? 800πm³.

Lesson 4 1 part 2 exponent practice. 10 7 volume of prisms course 1 warm up warm up lesson presentation lesson presentation. Homework is to study for tomorrow s unit 3 test! 4th period should also complete the unit 3 mini post test. you may check the answer key below click to. 2 warm up exercises exle 1 find the volume of a solid find the volume of the solid. v bh 1 3 36 m 3 a.a. 4 6 9 1 3 1 2.

Homework Practice Surface Area of Triangular Prisms Find the surface area of each triangular prism. Round to the nearest tenth if necessary. 6 km 14 km 6 km 2.6tt 70.2 ft2 4. 6 mm 8 mm 25 mm 6.5 mm 135 mm2 6 km 5.2 km 283.2 km2 3. 12 in. 164 in. 17 in. 24 in. 23.2 in. 1 ,636.8 in2 5. One foam block on the playground at Teeny Tots Preschool is ...

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