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Answer :
To find the approximate height of the cylindrical vase, we can follow these steps:
1. Understand the formula: The volume [tex]\( V \)[/tex] of a cylinder is calculated using the formula:
[tex]\[
V = \pi \times r^2 \times h
\][/tex]
where [tex]\( r \)[/tex] is the radius of the base, [tex]\( h \)[/tex] is the height, and [tex]\(\pi\)[/tex] is approximately 3.14.
2. Calculate the radius: The diameter of the vase is given as 6.2 inches. The radius [tex]\( r \)[/tex] is half of the diameter:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{6.2}{2} = 3.1 \text{ inches}
\][/tex]
3. Calculate the area of the base: The area of the circular base can be found using the formula for the area of a circle [tex]\( A = \pi \times r^2 \)[/tex]:
[tex]\[
A = 3.14 \times (3.1)^2 = 3.14 \times 9.61 \approx 30.18 \text{ square inches}
\][/tex]
4. Find the height: We are given the volume [tex]\( V \)[/tex] of the cylinder as 398.6 cubic inches. To find the height [tex]\( h \)[/tex], we rearrange the formula for volume to solve for [tex]\( h \)[/tex]:
[tex]\[
h = \frac{V}{\pi \times r^2} = \frac{398.6}{30.18} \approx 13.2 \text{ inches}
\][/tex]
Therefore, the approximate height of the vase is 13.2 inches.
1. Understand the formula: The volume [tex]\( V \)[/tex] of a cylinder is calculated using the formula:
[tex]\[
V = \pi \times r^2 \times h
\][/tex]
where [tex]\( r \)[/tex] is the radius of the base, [tex]\( h \)[/tex] is the height, and [tex]\(\pi\)[/tex] is approximately 3.14.
2. Calculate the radius: The diameter of the vase is given as 6.2 inches. The radius [tex]\( r \)[/tex] is half of the diameter:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{6.2}{2} = 3.1 \text{ inches}
\][/tex]
3. Calculate the area of the base: The area of the circular base can be found using the formula for the area of a circle [tex]\( A = \pi \times r^2 \)[/tex]:
[tex]\[
A = 3.14 \times (3.1)^2 = 3.14 \times 9.61 \approx 30.18 \text{ square inches}
\][/tex]
4. Find the height: We are given the volume [tex]\( V \)[/tex] of the cylinder as 398.6 cubic inches. To find the height [tex]\( h \)[/tex], we rearrange the formula for volume to solve for [tex]\( h \)[/tex]:
[tex]\[
h = \frac{V}{\pi \times r^2} = \frac{398.6}{30.18} \approx 13.2 \text{ inches}
\][/tex]
Therefore, the approximate height of the vase is 13.2 inches.
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