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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Answers

GPT-4o mini
To find the volume of the cylindrical vase, we will follow the formulas you provided step by step.

1. **Find the radius of the circular base**:
- The diameter of the vase is given as 8 inches. The radius \( r \) is half of the diameter.
\[
r = \frac{8}{2} = 4 \text{ inches}
\]

2. **Calculate the area of the circular base**:
- The area \( A \) of a circle is calculated using the formula:
\[
A = \pi r^2
\]
Here, we will use \( \pi = 3.14 \).
\[
A = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ square inches}
\]

3. **Height of the cylinder**:
- The height \( h \) of the cylinder is given as 10 inches.

4. **Calculate the volume of the cylinder**:
- The volume \( V \) of a cylinder can be calculated using the formula:
\[
V = A \times h
\]
Substituting in the values we have calculated:
\[
V = 50.24 \times 10 = 502.4 \text{ cubic inches}
\]

Putting all this together:
- 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**.

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