You have three small cylinders that are stored in a larger c

You have three small cylinders that are stored in a larger cylinder. Each of the smaller cylinders has a diameter of 6 in. and a height of 1 ft. The larger cylinder has a radius of 11.5 in. and a height of 3 ft. How much empty volume (space) is there when the three cylinders are in the larger cylinder?

Solution

Solution:

Total empty volume occupied inside the larger cylinder = volume of larger cylinder - 3 x volume smaller cylinder

= r_l² h_l - 3 * r²_sh_s

r_l =radius of larger cylinder and h_l= height of larger cylinder

r_s= radius of smaller cylinder and h_s = height of smaller cylinder

Total empty volume occupied inside the larger cylinder = ( 11.5² * 3 - 3* 3²*1)

= (369.75)

   = 1161.60 ft³

^{Answer =}1161.60 ft³