Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk and Adena Benn
Last updated: Oct 02, 2022
Thanks to our rectangular prism calculator, you can easily find the cuboid volume, surface area, and rectangular prism diagonal. Whether you are wondering how much water your fish tank holds or trying to find out how much paper you need to wrap a gift, give this rectangular prism calculator a go! If you are still unsure how it works, keep scrolling to learn about rectangular prism formulas.
What is a rectangular prism?
A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.
The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.
How do I find the volume of a rectangular prism?
The rectangular prism volume formula is:
volume = h × w × l,
where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:
- Find the box length. For example, it can be equal to 18 in.
- Determine its width. Let's say you measured 12 in.
- Find out the rectangular prism height. Assume it's 15 in.
- Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.
How do I find the area of a rectangular prism?
The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:
surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),
where h is prism height, w is its width, and l is its length.
Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:
- Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
- Or save yourself some time and use our rectangular prism calculator.
Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.
How do I calculate the diagonal of a rectangular prism?
To determine the diagonal of a rectangular prism, apply the formula:
diagonal = √(l² + h² + w²)
where h is prism height, w is its width, and l is its length.
Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.
How to calculate volumes of the other solids?
That rectangular prism was a piece of cake! If you are amazed at how easily you can calculate the volume with our tool, try out the other volume calculators:
- triangular prism calculator
- cylinder volume calculator
- sphere volume calculator
- cone volume calculator
- pyramid volume calculator
Be sure to check out the volume calculator - the volume of basic 3D solids, all in one place!
Hanna Pamuła, PhD candidate
Area of a hemisphereCubeCube Calc: find v, a, d… 17 more
You see it in boxes as you grab a tissue or pop open your box of cereal. You see it in books as you remove your bookmarks to begin reading. You see it in laptops as
you finish typing your latest assignment. Yes, we are talking about the rectangular prism. A rectangular prism is a three-dimensional shape with six faces. All the faces (top, bottom, and lateral faces) of the prism are rectangular so that all the pairs of opposite faces are congruent. It is also known as a cuboid. In short, a rectangular prism has four rectangular faces and two parallel rectangular bases. How is a rectangular prism different from a
rectangle? To begin with, why is it important to know the difference between different types of shapes? Every shape has distinct properties and these properties help to know quantities such as volume, surface area, etc. Remember, you would not know to not put a rectangle on top of a triangle if you don’t know how they are different. Now that we know what rectangular prisms are, let’s look at how we can calculate its volume. By multiplying the base area of a prism by its height, you will get the volume of a prism. That is to say, the volume of a prism = base area × height. Since a rectangular prism’s base is a rectangle itself, the volume of a rectangular prism, by
applying the formula given above, will be: Volume of a rectangular prism (V) = l× w× h Where, “l” means the base length, and “w” means the base width, “h” means the height Example 1: Find out
the volume of a rectangular prism with base length 9 inches, base width 6 inches, and height 18 inches, respectively. Solution: Here, Length (l) = 9 inches Width (b) = 6 inches Height (h) = 18 inchesDifference Between Rectangle & Rectangular Prism
Rectangle
Rectangular Prism
It is a 2D shape.
It is a 3D shape.
It has four sides.
It has six faces, eight verticals & twelve edges.
It is made of four sides with the opposite sides having equal lengths.
It is made up of six rectangles put together.
It has width and length.
It has width, height and length.
It is made of two pairs of lines.
It is made of three pairs of rectangles.
The Formula for Volume of a Rectangular Prism
Solved Examples
So, the volume of the given rectangular prism = l × w × h = 9 × 6 × 18 = 972 cubic inches.
Example 2: Find out the height of a rectangular prism whose base area is 20 sq. units and a volume is 60 cubic units.
Solution:
Given is the base area of the rectangular prism = 20 sq. units
And the volume of the rectangular prism = 60 cubic units
Now, applying the volume of the rectangular prism formula,
base area × height = 60 cubic units.
⇒ 20 × height = 60
⇒ height = 60 ÷ 20 units
⇒ height = 3 units
Example 3: Find out the base area of a rectangular prism with the help of the given measurements: length = 12 inches, height = 20 inches, and volume = 2,160 cubic inches.
Solution:
Here,
Length (l) = 12 inches
Height (h) = 20 inches
Volume (V) = 2,160 cubic inches
The volume of the rectangular prism = l × w × h
⇒ 2,160 = 12 × w × 20
⇒ 2,160 ÷ (12 × 20) = w
⇒ 9 = w
Therefore, width (w) = 9 inches.
Area = l × w = 12 × 9 = 108 sq. inches.
Practice Problems
V = Base area – height
V = Base area + height
V = Base area × height
V = Base area / height
Correct answer is: V = Base area × height
This essentially means the area of a rectangular prism is length × breadth × height as the base of the rectangular prism is a rectangle.
7 sq. inches
2,401 sq. inches
49 sq. inches
21 sq. inches
Correct answer is: 49 sq. inches
Base area of
rectangular prism = Volume ÷ Height = 343 ÷ 7 = 49 sq. inches
345 cubic cm
350 cubic cm
354 cubic cm
360 cubic cm
Correct answer is: 350 cubic cm
Volume of rectangular prism = base area × height = (35 × 10) = 350 cubic cm
Conclusion
The volume of a rectangular prism is an important concept for 5th graders to learn. As we have already discussed, the volume of a rectangular prism is the product of its dimensions, i.e., length, width, and height. This can be better understood with practical examples. Using SplashLearn, students can practice each example with online interactive worksheets. This game-based learning app makes learning fun and keeps your child engaged.
Every game on SplashLearn is curriculum-based and scientifically designed. To boost your kid’s knowledge in mathematics and allow them to practice mathematics fearlessly, you can sign up to SplashLearn for free!
Frequently Asked Questions
What is another name for a rectangular prism?
A rectangular prism is also known as a cuboid.
Is the volume of a rectangular prism the same as a cuboid?
Yes, the volume of a rectangular prism is the same as the volume of a cuboid.
What is an oblique rectangular prism?
An oblique rectangular prism is a prism with six rectangular faces, but the lateral faces are not perpendicular to the bases.
What is the surface area of a rectangular prism?
The surface area of a rectangular prism is the sum of the area of each of its faces. It is given by the formula, 2(lw + wh + hl), where l is length, w is width, and h is the height of the rectangular prism.