The volume of a cylinder: [tex]$V=\pi r^2 h$[/tex]
a) [tex]$72 cm^3$[/tex]
b) [tex]$18 cm^3$[/tex]
c) [tex]$40 cm^3$[/tex]

The volume of a cylinder is given by V = π r 2 h .
Any positive value can be a possible volume since the radius r and height h can be any positive real numbers.
For each given volume, we can find a corresponding height when setting the radius to 1.
Therefore, all three volumes are possible: a) 72 c m 3 , b) 18 c m 3 , and c) 40 c m 3 .

Explanation

Problem Analysis The problem states the formula for the volume of a cylinder, V = π r 2 h , and asks whether the given values are possible volumes. Since the radius r and height h can be any positive real numbers, any positive value of V is possible. Therefore, all three given values are possible volumes of a cylinder.

Verification for option a) For option a) V = 72 cm 3 , we can choose r = 1 and solve for h :
72 = π ( 1 ) 2 h h = π 72 ​ ≈ 22.92 cm So, a cylinder with radius 1 cm and height π 72 ​ cm has a volume of 72 c m 3 .

Verification for option b) For option b) V = 18 cm 3 , we can choose r = 1 and solve for h :
18 = π ( 1 ) 2 h h = π 18 ​ ≈ 5.73 cm So, a cylinder with radius 1 cm and height π 18 ​ cm has a volume of 18 c m 3 .

Verification for option c) For option c) V = 40 cm 3 , we can choose r = 1 and solve for h :
40 = π ( 1 ) 2 h h = π 40 ​ ≈ 12.73 cm So, a cylinder with radius 1 cm and height π 40 ​ cm has a volume of 40 c m 3 .

Conclusion Since we can find a corresponding height for each volume when r = 1 , all three volumes are possible.


Examples
Cylinders are commonly used in everyday life, from cans of soup to pipes in plumbing. Understanding how to calculate the volume of a cylinder is essential for determining how much a container can hold or how much material is needed to construct a cylindrical object. For example, if you're designing a cylindrical storage tank, you need to know its volume to ensure it can hold the required amount of liquid or gas. This involves using the formula V = π r 2 h to find the volume based on the tank's radius and height.

Answered by GinnyAnswer | 2025-07-03

All three given volumes (72 cm³, 18 cm³, and 40 cm³) are possible for a cylinder according to the formula V = π r 2 h . This is valid since we can always find a height for each volume by setting the radius to any positive value. Thus, there are no limitations in achieving these volumes given the formula.
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Answered by Anonymous | 2025-07-04