Please help with this

Question

Rose has a spherical plum of radius 2 and a spherical watermelon of radius 8. She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible. When she has done this, the volume contained within the sphere, but not in the plum or the watermelon, is . What is the value of ?

Answer 1

V=(4/3)(pi)(r^3) gives the volume of a sphere

plum: V=(4/3)(pi)(8)=(32/3)(pi)

watermelon: V=(4/3)(pi)(512)=(2048/3)(pi)

glass sphere has a diameter of 2+2+8+8=20 so radius is 10

glass sphere: V=(4/3)(pi)(1000)=(4000/3)(pi)

(4000/3)(pi)-(32/3)(pi)-(2048/3)(pi)=(1920/3)(pi)=640(pi)

K=640 cubic units