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Volume of Parallelepiped Formula

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  • Difficulty Level : Basic
  • Last Updated : 23 May, 2022
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A parallelepiped is defined as a three-dimensional shape formed by six parallelograms. It consists of six faces, eight vertices, and twelve edges. The face diagonals of a parallelepiped are two diagonals on each face. It has 12 face diagonals in total. The body or space diagonal of a parallelepiped is the diagonal connecting the vertices that are not on the same face. It can be interpreted as a prism with a parallelogram-shaped base. One of its every two faces is a mirror image of the other.

 

Volume of a parallelepiped formula

The volume of a parallelepiped is defined as the space filled by it in a three-dimensional plane. Knowing the base area and height of the parallelepiped is enough to calculate its volume. It is equal to the product of its base area and height.

V =  B × h

where,

V is the volume,

B is the base area,

h is the height.

Sample Problems

Problem 1. Calculate the volume of a parallelepiped if its base area is 20 m2 and height is 4 m.

Solution:

We have,

B = 20

h = 4

Using the formula we get,

V =  B × h

= 20 (4)

= 80 m3

Problem 2. Calculate the volume of a parallelepiped if its base area is 15 m2 and height is 3 m.

Solution:

We have,

B = 15

h = 3

Using the formula we get,

V =  B × h

= 15 (3)

= 45 m3

Problem 3. Calculate the volume of a parallelepiped if its base area is 23 m2 and height is 6 m.

Solution:

We have,

B = 23

h = 6

Using the formula we get,

V =  B × h

= 23 (6)

= 138 m3

Problem 4. Calculate the base area of a parallelepiped if its volume is 100 m3 and height is 5 m.

Solution:

We have,

V = 100

h = 5

Using the formula we get,

V =  B × h

=> B = V/h

= 100/5

= 20 m2

Problem 5. Calculate the base area of a parallelepiped if its volume is 350 m3 and height is 7 m.

Solution:

We have,

V = 350

h = 7

Using the formula we get,

V =  B × h

=> B = V/h

= 350/7

= 50 m2

Problem 6. Calculate the height of a parallelepiped if its volume is 3375 m3 and the base area is 225 m2.

Solution:

We have,

V = 3375

B = 225

Using the formula we get,

V =  B × h

=> h = V/B

= 3375/225

= 15 m

Problem 7. Calculate the height of a parallelepiped if its volume is 600 m3 and the base area is 120 m2.

Solution:

We have,

V = 600

B = 120

Using the formula we get,

V =  B × h

=> h = V/B

= 600/120

= 5 m

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