The volume of a rectangle-shaped prism is the measure of the room the filling it. In this article, you will find out how to uncover a rectangular prism volume by making use of the volume the a rectangle-shaped prism formula. We will also discuss the volume of a spherical cylinder.

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How to uncover the Volume that a rectangle-shaped Prism?

A rectangular prism is a 3-dimensional object through six rectangle-shaped faces. A rectangle-shaped prism is likewise referred to as a cuboid, rectangular hexahedron, right rectangular prism, or a rectangular parallelepiped.

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To uncover the volume of a rectangular prism, multiply the length, width, and height. The unit because that measuring the volume that a rectangle-shaped prism is cubic units, i.e., cm3, mm3, in3, m3, etc.

Volume of a rectangle-shaped Prism Formula

The formula because that the volume the a rectangle-shaped prism is provided as:

Volume that a rectangular prism = (length x width x height) cubic units.

V = (l x w x h) cubic units

In a rectangle-shaped prism, the product of the length and also the width is known as the base area. Therefore, us can also represent the volume of a rectangular prism formula as:

Volume that a rectangle-shaped prism = basic area x height

Let’s try the formula by functioning out a couple of example problems.

Example 1

The length, width, and also height of a rectangular prism are 15 cm, 10 cm, and 5 cm, respectively. What is the volume that the prism?

Solution

Given, size = 15 cm,

width = 10 cm,

height = 5 cm.

By the volume of a rectangular prism, we have

Volume = l x w x h

= (15 x 10 x 5) cm3

= 750 cm3.

Example 2

The volume that a rectangle-shaped prism is 192 cm3. If the prism’s size is double the height and width the 6 cm, find the dimensions of the rectangle-shaped prism.

Solution

Given,

Let the height be x.

Length = 2x

Width = 6 cm.

Volume = 192.

By volume the a rectangular prism,

⇒ 192 = x(2x) (6)

⇒ 192 = 12x2

On separating both sides by 12, us get

⇒ 16 = x2

⇒ x = 4, -4

Substitute

Length = 2x ⇒ 2x 4 =8 cm

Height = x ⇒ 4 cm

Therefore, the size of the rectangular prism room 8cm, 6cm, and also 4 cm.

Example 3

The length and also width that a rectangle-shaped aquarium are 800 mm and also 350 mm. When fish is presented in the aquarium, the water level rises by 150 mm. Uncover the volume that the fish.

Solution

The volume the the fish = the volume of the water displaced.

Volume the the fish = 800 x 350 x 150 mm3

= 4.2 x 107 mm3

Example 4

A rectangle-shaped water tank is 80 m long, 50 m wide, and also 60 m in height. If the water’s depth in the tank is 45 m, discover the volume that water compelled to fill the tank?

Solution

To uncover the water volume essential to to fill the tank, subtract the available water volume from the volume that water when the tank is full.

Volume that water, once the tank is full = 80 x 50 x 60

= 240,000 m3

Volume that the water available = 80 x 50 x 45

= 180,000 m3

Volume of the water compelled = (240,000 – 180,000) m3

= 60,000 m3

Example 5

The volume and also base area that a rectangular cargo container is 778 m3 and 120 m2. Find the height of the container?

Solution

Volume of a rectangle-shaped prism = base area x height

778 = 120 x height

Divide 120 on both sides.

778/120 = height

height = 6.48 m

So, the height of the container is 6.48 m.

Example 6

Small crate of measurement 1 m x 4 m x 5 m are to be packed in a bigger rectangular container of dimension 8 m x 10 m x 5 m. Discover the maximum variety of small boxes that can be pack in the container?

Solution

To find the variety of boxes to be packed, division the container’s volume by the volume that the box.

Volume of the container = 8 x 10 x 5

= 400 m3.

Volume of box = 1 x 4 x 5

= 20 m3

Number of box = 400 m3/20 m3.

= 20 boxes.

Example 7

The external dimensions that a wood box i m sorry is open up at the optimal is provided as 12 centimeter long, 10 cm vast and by 5 centimeter height. If the wall surfaces of the box room 1 centimeter thick, uncover the volume of the box

Solution

Find the interior dimensions of the box

Length = 12 – (1 x 2)

= 10 cm

Width = 10 – (1 x 2)

= 8 cm

Height = 5 centimeter – 1 …… (open at the top)

= 4 cm

Volume = 10 x 8 x 4

= 320 cm3.

Example 8

What room the dimensions of a cube with the very same volume together a rectangle-shaped prism with the dimensions together 8 m through 6 m by 3 m?

Solution

Volume that a rectangle-shaped prism = 8 x 6 x 3

= 144 cm3

So, a cube will likewise have a volume of 144 cm3

Since we understand that the volume that a cube = a3

where a is the size of a cube.

144 = a3

3√ a3 = 3√144

a = 5.24

Therefore, the dimensions of the cube will be 5.24 cm by 5.24 centimeter by 5.24 cm.

Example 9

Calculate the volume of a solid rectangle-shaped prism whose base area is 18 in2 and height is 4 in.

Solution

Volume that a rectangle-shaped prism = length x broad x height

= base area x height

V= 18 x 4

= 72 in3.

Example 10

Find the base area of a rectangle-shaped prism whose volume is 625 cm3 and also height is 18 cm.

Solution

Volume = base area x height

625 = base area x 18

By separating both sides by 18, us get

Base area = 34.72 cm2

Practice Questions

How perform you recognize a prism?

A. It has actually length, height, and width of equal or uneven lengths.

B. It has actually length, height, and also width of uneven lengths.

C. It has length, height, and also width of same or uneven lengths.

D. No one of these.

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2. Which of the adhering to is not a prism?

A. Organization box

B. Football

C. Dice

D. No one of these

3. How many cubic meter of water a rectangular prism-shaped swim pool have the right to hold, which is 12 meters long, 5 meter wide, and also 1.5 meter deep?

4. James has a music box v a height of 12.5 cm and also a base area that 75 square cm. Find the volume the the musical box.