To determine which water heater has the greatest volume, we can calculate the volume of each cylindrical storage tank using 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.
Let's calculate the volume for each water heater:
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Water Heater X:
- \( r = 8.5 \) inches
- \( h = 48 \) inches
\[ V_X = \pi (8.5)^2 (48) = \pi (72.25) (48) \approx 10916.5 \text{ cubic inches} \]
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Water Heater Y:
- \( r = 9.5 \) inches
- \( h = 44 \) inches
\[ V_Y = \pi (9.5)^2 (44) = \pi (90.25) (44) \approx 12566.5 \text{ cubic inches} \]
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Water Heater Z:
- \( r = 10.5 \) inches
- \( h = 32 \) inches
\[ V_Z = \pi (10.5)^2 (32) = \pi (110.25) (32) \approx 3492 \text{ cubic inches} \]
Now, let's summarize the approximate volumes:
- \( V_X \approx 10916.5 \)
- \( V_Y \approx 12566.5 \)
- \( V_Z \approx 3492.0 \)
From our calculations, we see that:
- Water Heater X has a volume of approximately 10916.5 cubic inches.
- Water Heater Y has a volume of approximately 12566.5 cubic inches.
- Water Heater Z has a volume of approximately 3492.0 cubic inches.
Thus, the statement D: "Water heater Y has the storage tank with the greatest volume" is true.
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