Answer:
57.4 cm³
Step-by-step explanation:
We will assume that the 3 balls are tightly packed inside the cylinder so that there is no space between each ball and the walls of the cylinder and there is no space between the bottom ball and the base of the cylinder as well as the top ball and the top of the cylinder
This means the cylinder has a diameter equal to the diameter of the ball = 2.9 cm
Therefore radius of the cylinder = diameter /2 = 2.9/2 = 1.45 cm
Since three balls can be vertically stacked up, the height of the cylinder is 3 times the diameter of each ball = 3 x 2.9 = 8.7 cm
The volume of the cylinder is given by the formula
V = πr²h where r is radius and h is the height
Plugging in known values on the right side we get
V = π · 1.45² · 8.7
Using value of pi =3.14 we get
V = 3.14 x 1.45² x 8.7
V= 57.436095 cm³
Rounded to the nearest tenth this would be 57.4 cm³
Answer:
57.4 cm³
Step-by-step explanation:
The packaging for 3 rubber balls is modelled as a cylinder.
If the balls have a diameter of 2.9 cm and are packaged one on top of another, then the diameter of the cylinder is equal to the diameter of one ball, and the height of the cylinder is equal to the sum of the diameters of all three balls.
Since the radius of a circle is half its diameter, the dimensions of the cylinder are:
The formula for the volume of a cylinder is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cylinder}}\\\\V=\pi r^2 h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
Substitute the values of r and h into the formula, and use 3.14 for π:
[tex]V = 3.14 \cdot 1.45^2 \cdot 8.7[/tex]
[tex]V = 3.14 \cdot 2.1025 \cdot 8.7[/tex]
[tex]V = 6.60185 \cdot 8.7[/tex]
[tex]V = 57.436095 \; \sf cm^3[/tex]
[tex]V = 57.4 \sf \; cm^3\;(nearest \;tenth)[/tex]
Therefore, the volume of the cylinder is about 57.4 cm³.
