A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 6 marbles, each of diameter 1 inch. The vase is filled with water up to a height of 12 inches.

What is the volume of water in the vase?

Question

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 6 marbles, each of diameter 1 inch. The vase is filled with water up to a height of 12 inches. 

What is the volume of water in the vase?

phi · Answer

Can you find the volume of the vase, up to a height of 12 inches?
V= area_of_base*height
the area of base is the area of a circle with a radius of 3 inches. A= pi r^2

Now you need to find the volume of a sphere with a radius of 1/2 inch.  subtract 6 of these from your vase volume to find how much water is in the vase.

anonymous · Answer

I got 190 but I know that's wrong...

anonymous · Answer

@phi is the answer 106pi in3

phi · Answer

First, how much water is in the cylinder if there were no marbles ?
use   radius = 3 inches  and height = 12 inches

anonymous · Answer

is there a formula @phi

phi · Answer

yes http://www.mathsteacher.com.au/year9/ch14_measurement/18_cylinder/cylinder.htm

anonymous · Answer

339.12 @phi

phi · Answer

ok ,  but don't multiply out the pi  (it looks nicer)
so just pi * 9 *12 =  108 pi   (which is about 339.12)

phi · Answer

now we have to find the volume of the marbles, because they are taking up room

V =  4/3  pi r^3

r is  1/2
can you find the volume of 1 marble  (and just leave pi in, don't multiply it )