Question

Please help!!
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 6 marbles, each of diameter 2 inches. The vase is filled with water up to a height of 12 inches.
What is the volume of water in the vase?

102π in3
106π in3
100π in3
108π in3

Answer 1

so you'd find the volume of a cylinder with the height of 12 inches, where the water is
and then
subtract the volume of the marbles

keep in mind that \(\bf \textit{volume of a cylinder}=\pi r^2 h\qquad h=height\qquad r=radius=\frac{diameter}{2}
\\ \quad \\
\textit{volume of a sphere or marble}=\cfrac{4}{3}\pi r^3\qquad r=radius=\frac{diameter}{2}\)

Answer 2

So I find the volume of a cylinder with a height of 12 and a diameter of 6 and then subtract the volume of the marbles?

Answer 3

And I get the volume of the marbles with the formula and then multiply that by six before subtracting, right?

Answer 4

yeap

the height of the water for the cylinder is 12
the radius is half the diameter, 6/2 = 3

the marbles have a diameter of 2
so their radius is 2/2 = 1

Answer 5

so where the marbles are, the water is NOT
so that space is NOT occupied by the 12inches high water area

so subtracting the marbles from it, will give only how much in water there is, or its volume

Answer 6

Thank you so much, you're a life saver