Question

Question

Sylvie has a cylindrical vase that is 10 inches tall and 8 inches wide. How many cubic inches of water will this vase hold?



Find the Volume of the vase. Use 3.14 for pi. Do not round.



Volume of Right Prism or Cylinder = (area of base)(height) or V = Bh

Area of a Circle = πr2



(4 points)
radius of the circular base =
inches

area of the circular base =
square inches

height of the cylinder =
inches

Volume of the cylinder =
cubic inches

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Answer 1

To find the volume of the cylindrical vase, we can use the formulas provided.

1. Calculate the radius of the circular base:

   • The diameter of the vase is 8 inches, so the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{8 \text{ inches}}{2} = 4 \text{ inches} \]

2. Calculate the area of the circular base:

   • Using the formula for the area of a circle, \( A = \pi r^2 \): \[ A = 3.14 \times (4 \text{ inches})^2 = 3.14 \times 16 \text{ square inches} = 50.24 \text{ square inches} \]

3. Height of the cylinder:

   • The height \( h \) of the vase is given as 10 inches.

4. Calculate the volume of the cylinder:

   • Using the formula for the volume of a cylinder, \( V = A \times h \): \[ V = 50.24 \text{ square inches} \times 10 \text{ inches} = 502.4 \text{ cubic inches} \]

Summary:

• 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