To determine the volume of the cylindrical vase, we’ll use the given formulas and dimensions.
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Find the radius of the circular base: The width of the cylinder is given as 8 inches. The radius (r) is half of the diameter (width). \[ r = \frac{\text{diameter}}{2} = \frac{8 \text{ inches}}{2} = 4 \text{ inches} \]
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Find the area of the circular base: The area (A) of the circle is given by the formula: \[ A = \pi r^2 \] Substituting in the values: \[ A = 3.14 \cdot (4 \text{ inches})^2 = 3.14 \cdot 16 \text{ square inches} = 50.24 \text{ square inches} \]
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Identify the height of the cylinder: The height (h) is given as 10 inches.
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Find the volume of the cylinder: The volume (V) is given by: \[ V = Bh = A \cdot h \] Substituting in the values: \[ V = 50.24 \text{ square inches} \cdot 10 \text{ inches} = 502.4 \text{ cubic inches} \]
Now we can summarize the answers:
- Radius of the circular base: 4 inches
- Area of the circular base: 50.24 square inches
- Height of the cylinder: 10 inches
- Volume of the cylinder: 502.4 cubic inches
Thus, the vase will hold 502.4 cubic inches of water.