A right rectangle-shaped prism is a three-dimensional solid form with 6 faces, 12 edges, and 8 vertices. That is additionally called a cuboid. The six faces of a right rectangular prism are rectangle-shaped in shape. Some examples of a right rectangular prism space books, aquarium, bricks. Similar to other two-dimensional and also three-dimensional shapes, the right rectangular prism additionally has a surface ar area.

You are watching: What is the volume of the right rectangular prism?

1.Right rectangular Prism Definition
2.Formulas the a Right rectangular Prism
3.Rectangular Prism Net
4.FAQs on Right rectangular Prism

Right rectangle-shaped Prism Definition


A right rectangle-shaped prism is a three-dimensional shape with six encounters (with every the 6 faces being rectangular in shape), 12 edges and also 8 vertices. Every the encounters of the prism space rectangles. All the angles created at the vertices room of 90° or ideal angles.

*

Properties that a Right rectangular Prism

It is an extremely easy to recognize a right rectangle-shaped prism if we recognize its simple properties. Provided below are its properties.

All its deals with are rectangles.Each edge of the prism to represent a right angle.

Formulas that a Right rectangular Prism


To find the surface area, volume, and length that the diagonal of a right rectangle-shaped prism, it is simple if we apply some formulae to do our calculations easier. Let united state learn about each the the formulas concerned the right rectangle-shaped prism in this section.

Surface Area that a Right rectangle-shaped Prism

Surface area is the room occupied by the external surface of any type of solid shape. The surface ar area of a right rectangle-shaped prism is the space occupied by all the faces of the right rectangular prism.

Surface area that a right rectangular prism = lw+lw+wh+wh+lh+lh, i m sorry is equal to 2(lw+wh+lh) square units.

*

Surface Area = 2(lw+wh+lh) square units.

Volume of Right rectangular Prism

Volume is the an are occupied by a closed surface of a solid shape. Volume the a right rectangular prism can be identified as the product that the area that one challenge multiplied by its height.

*

The volume the a right rectangular prism (V) for a length (l), height (h), and width (w) is given by,Volume = (l × w × h) cubic units.

Diagonal of a Right rectangle-shaped Prism

A diagonal line is a line the joins 2 opposite corners the a shape that has actually straight sides. The diagonal line of a right rectangular prism is the square root of the sum of the squares the the length, width, and also height.

*

The diagonal line of a right rectangular prism of length (l), broad (w), and also height (h) is given by,

Diagonal = (sqrtl^2+w^2+h^2)

Important Notes

A rectangular prism has actually six encounters - the base, the top, and also the four sides.The base and also top always have the same area. The pairs of the opposite sides have actually the same area together well.The volume of rectangle-shaped Prism: V = lwhSurface Area of rectangular Prism: S = 2(lw + lh + wh)In a right rectangular prism, edges = 12, deals with = 6, vertices = 8When all sides that a right rectangular prism space equal, that is called a cube. Its surface area is 6a2 and volume is a3.

Challenging Questions

Is a cube a rectangle-shaped prism?Can you identify the volume that a rectangular prism as soon as the area of its base and height space given yet the length and width space not offered as different measurements?

A net is characterized as a design of a two-dimensional shape that can be folded and also made right into a three-dimensional shape. The network of any kind of geometrical three-dimensional form is derived by unfolding it follow me its edges and faces. The net of the right rectangle-shaped prism is same to its surface area. The photo given below shows the network of a rectangular prism. We can clearly observe that it is comprised of rectangles. By calculating the area of each rectangle, and adding them up us can find the net or the surface area of the right rectangular prism.

*

Topics concerned Right rectangular Prism

Check out these interesting posts to know more about right rectangle-shaped prism.


Example 1: Emily needs to buy part cardboard to construct a box without a lid. She wants the box to measure up 7 devices long, 5 devices wide, and 9 units high. Just how much cardboard have to she buy?

Solution:

The dimensions of the box are as follows: length l = 7 devices Width w = 5 units elevation h = 9 units

We will determine the surface area the the open box, that is, without a lid.

The surface area that the open box is: lw+2wh+2lh = 7 × 5 + 2 × 5 × 9 + 2 × 7 × 9= 35+90+126= 251 square unitsTherefore, Emily should buy 251 square systems of cardboard.


Example 2:

Identify the right rectangle-shaped prisms native the following.

*
Solution: For an object to it is in a right rectangle-shaped prism, the should have actually all six faces as rectangles, the opposite encounters should it is in equal and the cross-section follow me the length is the same. Because all the over conditions space satisfied, we can say that all 3 are similar to a right rectangle-shaped prism.


Example 3: Kevin desires to recognize the height of a rectangular prism v base area 10 units2 and volume 40 units3.Solution:

The volume of a rectangular prism is 40 cubic units. The base area is given by l×b = 10 square units. The elevation of the prism is calculated together follows.

Volume = 40 cubic units

So, lbh = 40

lb × h = 40

10 × h = 40

h = 4 unitsTherefore, elevation of the prism is 4units.


Example 4: Tim want to add soil come his gardening bed i m sorry is in the shape of a rectangle-shaped prism and also has the following dimensions: size = 8 units, width = 4 units, and also height = 1 units. What is the maximum quantity of planting soil that can be used to fill the gardening bed?

*
Solution:

Tim's gardening bed resembles that of a rectangular prism having actually the complying with dimensions: Length, l = 8 devices Width, w = 4 units and Height, h = 1 unit.

See more: Zeke And Luther Theme Song Lyrics (Hd), Zeke And Luther Theme Song

The maximum quantity of planting soil that deserve to be used to to fill the bed is the volume of the bed i beg your pardon is equal to = (l × w × h) cubic units. That is, 8 x 4 x 1 = 32 cubic units. Therefore, 32 cubic systems of the soil can be used to fill the gardening bed.