Volume of Parallelepiped Formula
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.
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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
Last Updated :
24 Jan, 2024
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