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 [tex] 10\pi [/tex] [tex] in^3 [/tex] and the height is 8 inches.
Therefore, Volume of Sand=[tex] 10\pi \times 8=80\pi [/tex] [tex] in^3 [/tex]
Now, for calculating the volume of water, we will employ the formula:
Volume=[tex] \pi [/tex]x[tex] (radius of the circular bottom)^2 [/tex]xheight
Thus, from the given data, Volume of water is:
[tex] \pi\times(2)^2 \times 5=20\pi [/tex] [tex] in^3 [/tex]
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 [tex] (80\pi-20\pi) [/tex]=[tex] 60\pi [/tex] [tex] in^3 [/tex].
