To find the volume of the cylinder, we can use the formula for the volume \( V \) of a cylinder, which is:
\[ V = B \cdot h \]
where \( B \) is the area of the base and \( h \) is the height of the cylinder.
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Determine the radius:
The diameter of the base is given as 4 cm, so the radius \( r \) is:
\[ r = \frac{d}{2} = \frac{4 , \text{cm}}{2} = 2 , \text{cm} \]
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Calculate the area of the base \( B \):
The area \( B \) of the base, which is a circle, is given by the formula:
\[ B = \pi r^2 \]
Plugging in the radius:
\[ B = \pi (2 , \text{cm})^2 = \pi \cdot 4 , \text{cm}^2 = 4\pi , \text{cm}^2 \]
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Determine the height \( h \):
The height \( h \) is given as 7 cm.
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Calculate the volume \( V \):
Now we can plug the values of \( B \) and \( h \) into the volume formula:
\[ V = B \cdot h = (4\pi , \text{cm}^2) \cdot (7 , \text{cm}) = 28\pi , \text{cm}^3 \]
So, the volume of the cylinder in terms of \( \pi \) is:
\[ \boxed{28\pi , \text{cm}^3} \]