Sure, let's break down the problem step-by-step.
1. Identify the given values:
- Height of the vase (h) = 12 inches
- Diameter of the vase (d) = 4 inches
- We will use 3.14 as an approximation for π (pi).
2. Calculate the radius of the vase:
- The radius (r) is half of the diameter.
- [tex]\( r = \frac{d}{2} = \frac{4}{2} = 2 \)[/tex] inches
3. Use the formula for the volume of a cylinder:
- The formula for the volume (V) of a cylinder is [tex]\( V = \pi r^2 h \)[/tex].
- Substitute the known values into the formula:
[tex]\[
V = 3.14 \times (2^2) \times 12
\][/tex]
4. Calculate the area of the base:
- First, compute [tex]\( r^2 = 2^2 = 4 \)[/tex].
5. Calculate the volume:
- Now, substitute [tex]\( r^2 \)[/tex] into the formula:
[tex]\[
V = 3.14 \times 4 \times 12
\][/tex]
- Multiply the values:
[tex]\[
V = 3.14 \times 48 = 150.72 \text{ cubic inches}
\][/tex]
6. Round the volume to the nearest tenth:
- The volume 150.72 rounded to the nearest tenth is 150.7 cubic inches.
So, the radius of the vase is 2 inches, the unrounded volume is 150.72 cubic inches, and the volume rounded to the nearest tenth is 150.7 cubic inches.
