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Volume Of Rectangular Prism

Rectangular prisms are very common geometric shapes. I'm sure if you looked around your home or classroom right now, you would be overwhelmed with the appearance of this shape. Here are some common examples of rectangular prisms: books, handheld erasers, most buildings, candy bars. They are three dimensional objects that are composed of six sides and as a result they exert three measures of length (height, width, and length) Because they are a very common shape in transport, the space that they take up (volume) is one of the most common daily calculations on the planet. Ever see a tractor trailer before? Guess what the trailer is in the shape of? At any given time, there are believed to be well over 50 million shipping containers moving across the globe. To measure the volume of these containers we simply multiple their 3 measures of length (height x width x length). These worksheets will not only go over the fundamental uses of this measure and calculating it, we will explore volume word problems that incorporate this geometric shape.

Aligned Standard: Grade 6 Geometry - 6.G.A.2

  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

Some of these problems were really fun to write.

  • Homework 1 - A wall is 12m long, 9m wide, and 6m deep. John wants to know the volume of the wall because he wants to paint the wall. What is the volume of the wall?
  • Homework 2 - John buys a rectangular shaped bed for his sister. The bed is 14 feet long by 9 feet wide. John wants to put a cover on the bed, so he wants to know the area of the bed. What is the area?
  • Homework 3 - Robert has a cell phone box. The box is 19 inches long by 11 inches wide by 9 inches high. What is the volume of the box?

Practice Worksheets

I started all these problems by picking a cute clip art and working a problem off of it.

  • Practice 1 - Liza installs a huge bathtub in her bathroom. Her bathtub measures 15 meters in length, 25 meters in width, and 35 meters in height. What is the volume of the bathtub?
  • Practice 2 - Charles buys a table. His table has a length of 12 meters, a width of 17 meters, and a height of 24 meters. What is the volume of the table?
  • Practice 3 - John purchased a rectangular foot stool for the table. The stool has a length of 28 cm, a width of 19 cm, and a height of 40 cm. What is the volume of the stool?

Math Skill Quizzes

Each quiz works on a different set of shapes.

  • Quiz 1 - Jacob purchased a photo frame in a rectangular shape. The photo frame is 10 feet long by 6 feet wide. Jacob wants to know the area of the photo frame. What is the area?
  • Quiz 2 - Emma eats a pizza slice. The height of the slice is 7 in and has a flat base of 10 in. Find the area of the slice?
  • Quiz 3 - John goes to the market and buys a book. The book is 30 inches long and 22 inches wide. What is the area of book?


Where Do You Find Rectangular Prisms in Real Life?

These geometric shapes are characterized as three-dimensional shapes that six rectangle-based faces. They also have three common properties held between them. They all have eight vertices and twelve sides. All the opposite faces on this shape are equal. If you take a cross section of these shapes, they will be rectangular in shape as well. Due to these properties this shape is widely used in the packaging and shipping communities because it provides a sturdy and consistent design to hold up in what ever conditions are thrown at it. Shipping containers are the modelled after this shape. Ninety-five percent of the world's cargo travels around the world these. From the ship to the back of tractor trailer trucks to the store or warehouse near you. This shape is also found in your favorite aquariums due to the consistent design, the pressure created by the water evenly pushes on the walls making for a very stable structure. This figure is at the center of most high-rise buildings. Any design that requires stability and uniformity will usually lend itself to adapting this geometric shape within it at some point.


How To Find The Volume Of A Right Rectangular Prism

Right rectangular prisms are three-dimensional solid shapes. This a familiar shape to you. You find that textbooks, playing dice, doors, bricks, even your phone is most likely this shape. They have six sides and as a result there are twelve edges on them as well.


You are now about to learn a new mathematical concept. It is the volume of this wonderfully familiar shape. To find out the volume first, you need to what is volume. It is the 3-dimensional space of an object that it occupies when kept in a place. It takes three-dimensions to calculate the volume which is composed of the measures: length, height, and width. If we are measuring real physical shapes the units are all found in a length measurement unit, but they are measured in cubic units. This is because we are compounding the measures of three dimensions.


When it comes to finding the volume of a right rectangular prism, which is a solid geometric figure that has vertical sides perpendicular to the base, this prism is called a “right” prism because the angles between the base and sides are right angles. The formula is the same if you know the length, width, and height of the prism. Volume = l x w x h. Here, l = the length of the base of the prism, w = the width of the bottom of the prism, and h = the height of the lens.


Consider this example: Find the volume of a right rectangular prism having length three cubic units, width four cubic unit, and height five cubic unit. That is pretty easy: V = l x w x h, V = 3 x 4 x 5, V = 60 cubic unit.


Why not tackle a real-world problem that incorporates this with something that all of us volume a great deal, our mobile phone! You are about to take a kayak out on the river. You are warned by the kayak's owner that if your mobile phone measures more than 150 in3, you should not bring it as it will most likely crack against the side of the boat. If your mobile phone measures 10 inches, 2 inches, 6 inches, should you bring it with you kayaking?


dimensions of mobile phone

To determine the volume of this phone we would simply put the measures into the same old equation (l x w x h) that we have been using. 10 x 2 x 6 = 120 in3. Now that we have our calculation, we can make our decision on whether to bring out phone on the kayak. Since the volume is less than 1503, we can bring our phone kayaking with us. I would still encourage you to put it in something waterproof.


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