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 Kpi. What is the value of K?

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 =   × × 2³

                            = ×

Volume of watermelon

        = ×

Volume of glass sphere = × × R³

                                          = ×

So now the volume remaining inside the glass sphere  =  volume of glass sphere –( volume of plum + volume of watermelon)

==>  K × =   ×

==>  K ×  = ×

So K = 1820

Hence the value of K is 1820

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