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

Answer 1

To find the volume of Sylvie's cylindrical vase, we will follow these steps:

1. **Calculate the radius of the circular base:**
The width of the vase is given as 8 inches. Since the diameter of a circle is twice the radius, we can find the radius (r) as follows:
\[
r = \frac{\text{diameter}}{2} = \frac{8 \text{ inches}}{2} = 4 \text{ inches}
\]

2. **Calculate the area of the circular base:**
The area (A) of the circular base can be calculated using the formula:
\[
A = \pi r^2
\]
Substituting in the values:
\[
A = 3.14 \times (4 \text{ inches})^2 = 3.14 \times 16 \text{ square inches} = 50.24 \text{ square inches}
\]

3. **Height of the cylinder:**
Given that the height (h) of the vase is 10 inches, we have:
\[
h = 10 \text{ inches}
\]

4. **Calculate the volume of the cylinder:**
The volume (V) of the cylinder is given by the formula:
\[
V = A \times h
\]
Substituting the area we calculated and the height:
\[
V = 50.24 \text{ square inches} \times 10 \text{ inches} = 502.4 \text{ cubic inches}
\]

In conclusion:

- **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

These calculations show that the vase can hold **502.4 cubic inches of water**.