Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 2/3 for the flowers to last the longest. Her cylinder vase has a radius of 3 in and a height of 8 in. Using the equation below, how much water should Mary pour into the vase?
The volume of a cylinder with height h and radius r is given by the formula:
V=πr^2h
im still kinda confused
i dont think this really helped cus im confused...
To find the volume of the cylinder, we can use the formula:
V = πr^2h
Given that the radius (r) of the vase is 3 in and the height (h) is 8 in, we can substitute these values into the formula.
V = π * (3^2) * 8
= π * 9 * 8
= π * 72
≈ 226.195 in^3
So, the volume of the cylinder is approximately 226.195 cubic inches.
Now, Mary needs to fill the vase 2/3 full with water. To find out how much water that is, we can multiply the volume of the cylinder by 2/3.
Water volume = 226.195 in^3 * 2/3
= 150.797 in^3
Therefore, Mary should pour approximately 150.797 cubic inches of water into the vase.
Since the radius is constant, wouldn't the volume simply depend on the height of the water?
So Mary must fill it to a height of (2/3)(8) inches or 16/3 inches.
If you want the actual volume she had to pour in .....
Volume = (9π)(16/3) cubic inches
= 48π inches^3 or appr 150.8 cubic inches.
or:
volume of whole cylinder = π(9)(8) = 72π cubic inches
you want 2/3 of that which is (2/3)(72π) = 48π cubic inches
what height is that?
9π(h) = 48π
h = 48π/9π = 16/3 , just as above