In this publication, we will look at how you can find the volume of a prism and analyze examples of solving problems to fix the material.
The formula for calculating the volume of a prism
The volume of a prism is equal to the product of the area of its base and its height.
V=Smain ⋅ h
- Smain – base area, i.e. in our case, a quadrilateral ABCD or EFGH (equal to each other);
- h is the height of the prism.
The above formula is suitable for the following types of prisms:
- straight – side ribs are perpendicular to the base;
- correct – a direct prism, the base of which is a regular polygon;
- inclined – side ribs are located at an angle with respect to the base.
Examples of tasks
Task 1
Find the volume of the prism if it is known that the area of its base is 14 cm2and the height is 6 cm.
Decision:
We substitute the known values into the formula and get:
V=14cm2 ⋅ 6 cm = 84 cm3.
Task 2
The volume of the prism is 106 cm3. Find its height if it is known that the area of the base is 10 cm2.
Decision:
From the formula for calculating the volume, it follows that the height is equal to the volume divided by the area of uXNUMXbuXNUMXbthe base:
h = V / Smain = 106 cm3 / 10 cm2 = 10,6 cm.