Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.

Correct result:

V =  5322.6258 cm3

Solution:

r=8 R=6 x=2⋅ 10−r−R=2⋅ 10−8−6=6 h=(r+R)2−x2=(8+6)2−62=4 10≐12.6491 H=h+r+R=12.6491+8+6≐26.6491 V1=π⋅ 102⋅ H=3.1416⋅ 102⋅ 26.6491≐8372.065 V2=4/3π⋅ r3=4/3⋅ 3.1416⋅ 83≐2144.6606 V3=4/3π⋅ R3=4/3⋅ 3.1416⋅ 63≐904.7787 V=V1−V2−V3=8372.065−2144.6606−904.7787=5322.6258 cm3

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