Answer :
Volume of Sphere
The value of K is 1820
Step-by-step explanation:
Given the radius of plum R1 = 2 cm
Given the radius of watermelon R2 = 8 cm
Suppose the radius of the glass sphere be R
For the radius R to be minimum so as to contain both the plum and watermelon
R has to be equal to the sum of the 2 individual radii
that is R = R1 + R2
Accordingly the radius R = 2 + 8 = 10 cm
Volume of plum = [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex]× 2³
= [tex]\frac{32}{3}[/tex] × [tex]\pi[/tex]
Volume of watermelon
= [tex]\frac{2048}{3}[/tex] × [tex]\pi[/tex]
Volume of glass sphere = [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × R³
= [tex]\frac{4000}{3}[/tex] × [tex]\pi[/tex]
So now the volume remaining inside the glass sphere = volume of glass sphere –( volume of plum + volume of watermelon)
==> K × [tex]\pi[/tex] = [tex]\frac{4000 –(2048 + 32))}{3}[/tex] × [tex]\pi[/tex]
==> K × [tex]\pi[/tex] = [tex]\frac{1820}{3}[/tex] × [tex]\pi[/tex]
So K = 1820
Hence the value of K is 1820