Question

to find the volume of a shape, you need to know the__________and height.
the volume of a cylinder is always__________times the volume of a cone with the same height and radius.
when calculating volumes, the value of π is approximately__________
the unit of measurement for volume when using centimeters is__________
the height of a shape is denoted by the letter__________
the radius of the base of a shape is denoted by the letter__________
in real - world applications, understanding the volume of a cone or cylinder helps in__________
in the formula ( v=pi r^{2}h ), the letter ( v ) stands for__________

Explanation:

• For the first blank, the formula for the volume of many 3 - D shapes (like cylinder, cone) involves the area of the base and height. For example, \(V = B\times h\) where \(B\) is the area of the base.
• The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\) and for a cone \(V_{cone}=\frac{1}{3}\pi r^{2}h\). So, \(V_{cylinder} = 3V_{cone}\) when \(r\) (radius) and \(h\) (height) are the same.
• The approximate value of \(\pi\) is \(3.14\).
• When using containers, a common unit for volume is liters.
• In mathematical formulas, the letter \(h\) is used to denote height.
• In mathematical formulas, the letter \(r\) is used to denote the radius of the base.
• Understanding the volume of a cone or cylinder helps in tasks like filling containers (e.g., how much liquid a cylindrical tank can hold or how much ice - cream a conical cone can hold).
• In the formula \(V=\pi r^{2}h\), by the definition of the formula, \(V\) stands for volume.

Answer:

1. base area
2. \(3\)
3. \(3.14\)
4. liters
5. \(h\)
6. \(r\)
7. filling containers (a reasonable real - world application)
8. volume