To find the volume of the mug, which can be modeled as a cylinder, we use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
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Calculate the radius: The diameter of the mug is 9 centimeters, so the radius \( r \) is half of that: \[ r = \frac{9}{2} = 4.5 \text{ cm} \]
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Height of the mug: The height \( h \) of the mug is given as 11 centimeters.
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Calculate the volume: \[ V = \pi (4.5)^2 (11) \] First, calculate \( (4.5)^2 \): \[ (4.5)^2 = 20.25 \] Now substitute this back into the volume formula: \[ V = \pi (20.25)(11) \] Continue the calculation: \[ V = \pi (222.75) \] So the volume is approximately: \[ V \approx 3.14 \times 222.75 \approx 700.43 \text{ cm}^3 \]
Thus, the closest value to the volume of the mug is approximately \(\mathbf{700.43 , \text{cm}^3}\).