Sphere submerged in the cone

A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere.

Correct answer:

V =  0.0756 cm3

Step-by-step explanation:

D=24 cm h=8 cm r=3.0 cm  R=D/2=24/2=12 cm  α=arctan(R/h)=arctan(12/8)0.9828 rad tanα=r/s s=r/tanα=3/tan0.9828=2 cm cosα=h1:s sinα=r1:s  h1=s cosα=2 cos0.98281.1094 cm r1=s sinα=2 sin0.98281.6641 cm  sinα=r:h3 h3=r sinα=3 sin0.98282.4962 cm  h2=h1(h3r)=1.1094(2.49623)1.6132 cm  V1=31 π r12 h1=31 3.1416 1.66412 1.10943.2172 cm3 V2=π(r12+2 r1 h2)=3.1416(1.66412+2 1.6641 1.6132)3.1416 cm3  V=V1V2=3.21723.1416=0.0756 cm3

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