A tank in the shape of a cylinder of diameter 2.4 m and height 6.4 m contains oil to the brim. Find the number of complete cylindrical containers of base radius 8.2 cm and height 28 cm which can be filled by the oil in the tank.

Step-by-step explanation:

olume of the cylindrical portion of the tank= ttr²h

=22/7 * (21/2)2 * 18cm3 = 174636/ 28 m3

= 6237m3

volume of 2 conical ends

=2 (1/3 ttr2h) =2/3 ttr2h =2/3 * 22/7 * (21/2)2 * 9m3

=174636 / 84 m3 =2079m3

therefore, capacity of the tank= 6237m3 + 2079m3= 8316m³=83160000

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4