Volume of Prisms and Cylinders
Key Concepts
- Find the number of unit cubes.
- Find volumes of prisms and cylinders.
Introduction
Volume
Volume is the number of cubic units contained in a solid. It is measured in cubic units.
The basic formula is V = Bh, where B = area of the base, h = height.
Cubic Unit
Find the number of unit cubes
Example 1:
Find the volume of the puzzle piece shown in cubic units.
Solution:
To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows:
The base is 3 units by 1 unit. So, it contains 3 × 1, or 3 unit cubes.
The top layer is 3 units by 1 unit. So, it contains 3 × 1, or 3 unit cubes.
The upper left box is 1 unit by 1 unit1. So, it contains 1 × 1, or 1 unit cube.
By the Volume Addition Postulate, the total volume of the puzzle piece is 3 + 3 + 1 = 7 cubic units.
Example 2:
Find the volume of the solid in cubic units.
Solution:
To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows:
Front Layer:
Middle Layer:
Back Layer:
By the Volume Addition Postulate, the total volume of the solid is 11 + 11 + 11 =33 cubic units.
Find volumes of prisms and cylinders
Volume of a prism
The volume of a right rectangular prism is equal to the product of the height and the area of the base.
V = Bh
Where B is the area of the base and h is the height.
Volume of a Cylinder
The volume of a cylinder is equal to the product of the height and the area of the base.
V = Bh = πr2h
Where B is the area of the base, h is the height, and r is the radius of the base.
Example 3:
Find the volume of the following triangular prism.
Solution:
The area of a base is ½ (10)(8) = 40 and l = 3.
V = Area of a base x l
V = 40(3) = 120 cubic units
Example 4:
A soda can measures 5.5 inches high, and its diameter is 2.5 inches. Find the approximate volume.
Solution:
The diameter is 2.5 in. The radius is 2.5 ÷ 2 inches.
V = pr2h
V = p(1.252)(5.5)
V » 26.98 in3
Exercise
- Explain in your own words how to find the volume of a figure. Give an example.
- Find the volume of the given cube
- Find the volume of the figure.
- Find the volume of the figure.
- Find the volume of the figure.
- Find the volume of the figure.
- Find the volume of the figure.
- A birthday cake has three layers. The top cake has a diameter of 8 inches and is 3 inches deep. The middle cake is 12 inches in diameter and is 4 inches deep. The bottom cake is 14 inches in diameter and is 6 inches deep. Find the volume of the entire cake, ignoring the icing.
- Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet.
- Find the volume of the solid prism shown below.
Concept Map
What have we learned
- Find the number of unit cubes in the given solid shape.
- Find volume of a prism by using the formula.
- Find volume of a cylinder by using the formula.
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