What is a Parallelepiped?
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.
Find the Volume of a Parallelepiped?
To calculate the volume of a parallelepiped using the formula, it is essential to determine two measurements:
- S, representing the area of the base.
- H, denoting the height of the parallelepiped.
Solved Example for Rectangular Parallelepiped Formula
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
Related Topics:
- Equilateral Triangle Formula
- Percentile Formula
- Selling Price Formula
- Diameter Formula
- Volume Formulas
- Triangle Formula
- Cos Theta Formula
- Sin Cos Formula
- Pyramid Formula
Volume of Parallelepiped Formula – FAQs
What is a Parallelepiped and How Do You Calculate Its Volume?
A parallelepiped is a three-dimensional geometric figure with six parallelogram faces. The volume is calculated based on the area of the base parallelogram and the perpendicular height from the base to the opposite face. This calculation considers the alignment and dimensions of the sides.
What Factors Influence the Volume of a Parallelepiped?
The volume is influenced by the lengths of the edges and the angles between them. Specifically, it depends on the area of the base and the height relative to that base, with the orientation of the angles affecting how these measurements are used in the volume calculation.
Can You Describe the Role of Angles in Determining Parallelepiped Volume?
The angles between the edges of the base and between the base and the other faces are crucial. These angles help determine the effective height used in calculating the volume, as the height must be perpendicular to the base.
What Are Common Misconceptions About Calculating the Volume of a Parallelepiped?
A common misconception is that the volume can be found simply by multiplying the lengths of the three edges. Instead, the calculation must consider the spatial orientation of these edges and the true perpendicular height.
How is Parallelepiped Volume Applied in Real-world Contexts?
The volume calculation of a parallelepiped is vital in fields such as architecture, engineering, and physics. It helps in determining the capacity, space utilization, and material quantity in construction and design, as well as in various physics calculations involving vectors in space.