Question

Cindy has a cylindrical bucket filled with sand; the area of the circular bottom is 10pi inches and the hieght of the bucket is 8 inches. Candy has a nother cylinderal bucket filled with water; the raidus of the circular bottom is 2 inches and the ehight of the bucket is 5 inches. Is there more sand or water? What is the difference?

Answer 1

For the cylindrical bucket filled with sand, the volume of sand in the bucket will be given by the formula:

Volume=Area of the circular bottom x height

We know that the area of the circular bottom is given to be
`10\pi`
`in^3` and the height is 8 inches.

Therefore, Volume of Sand=
`10\pi * 8=80\pi`
`in^3`

Now, for calculating the volume of water, we will employ the formula:

Volume=
`\pi`x
`(radius of the circular bottom)^2`xheight

Thus, from the given data, Volume of water is:

`\pi*(2)^2 * 5=20\pi`
`in^3`

As can be clearly seen the volume of sand is more than the volume of water and thus there is more sand than water. The difference in their volumes is
`(80\pi-20\pi)`=
`60\pi`
`in^3`.