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Answer :
To find the volume of water in the vase, we first note that the vase is in the shape of a cylinder. The volume [tex]\( V \)[/tex] of a cylinder is given by the formula
[tex]$$
V = \pi r^2 h,
$$[/tex]
where [tex]\( r \)[/tex] is the radius of the base and [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- [tex]\( r = 2 \)[/tex] inches
- [tex]\( h = 8 \)[/tex] inches
1. Substitute the given values into the formula:
[tex]$$
V = \pi (2)^2 (8).
$$[/tex]
2. Calculate the square of the radius:
[tex]$$
(2)^2 = 4.
$$[/tex]
3. Multiply by the height:
[tex]$$
4 \times 8 = 32.
$$[/tex]
So the volume becomes
[tex]$$
V = 32\pi.
$$[/tex]
4. Using the approximation [tex]\( \pi \approx 3.14 \)[/tex], we calculate:
[tex]$$
V \approx 32 \times 3.14 = 100.48.
$$[/tex]
5. Rounding [tex]\( 100.48 \)[/tex] to the nearest tenth gives:
[tex]$$
V \approx 100.5 \text{ cubic inches}.
$$[/tex]
Thus, the volume of the water in the vase is approximately [tex]\( 100.5 \)[/tex] cubic inches.
[tex]$$
V = \pi r^2 h,
$$[/tex]
where [tex]\( r \)[/tex] is the radius of the base and [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- [tex]\( r = 2 \)[/tex] inches
- [tex]\( h = 8 \)[/tex] inches
1. Substitute the given values into the formula:
[tex]$$
V = \pi (2)^2 (8).
$$[/tex]
2. Calculate the square of the radius:
[tex]$$
(2)^2 = 4.
$$[/tex]
3. Multiply by the height:
[tex]$$
4 \times 8 = 32.
$$[/tex]
So the volume becomes
[tex]$$
V = 32\pi.
$$[/tex]
4. Using the approximation [tex]\( \pi \approx 3.14 \)[/tex], we calculate:
[tex]$$
V \approx 32 \times 3.14 = 100.48.
$$[/tex]
5. Rounding [tex]\( 100.48 \)[/tex] to the nearest tenth gives:
[tex]$$
V \approx 100.5 \text{ cubic inches}.
$$[/tex]
Thus, the volume of the water in the vase is approximately [tex]\( 100.5 \)[/tex] cubic inches.
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