Question

Wax cylinder of diameter 21 cm and height 21 cm is chipped off and shaped to form a cone of maximum volume the chipped of wax is the recast into a solid sphere. find the diameter of the sphere

Answer 1

HEYA ,

YOUR ANSWER IS IN ATTACHMENT,

●●CLARIFICATION ●●
[A cone of maximum volume can be chipped off only when the height and diameter of the cone is equivalent to height and diameter of cylinder.

Now, the wax remained after chipping off cone is recast to form a sphere.]●●

HOPE IT HELPS U !!!!

Answer 2

Wax cylinder of diameter 21cm and height 21cm is chipped off and shaped to form a cone of maximum volume the chipped of wax is the recast into a solid sphere. The diameter of the sphere is 21 cm.

Stepwise explanation is given below:

- It is given that the diameter of cylinder=21cm

- So, the radius =21/2cm

And height is also 21cm.

- Let us asume that the r1 is the radius of the sphere

- So,

volume of cylinder= volume of cone + volume of sphere

πr^2h=1/3πr^2h+4/3π(r1)^3

r^2h=1/3r^2h+4/3(r1)^3

- By putting there values. We get,

(21/2)^2(21)=(1/3)((21/2)^2(21)+4/3(r1)^3

4/3(r1)^3=(21/2)^2(21) - (1/3)((21/2)^2(21)

4/3(r1)^3=(2/3)(21/2)^2(21)

(r1)^3=(2/3)(21/2)^2(21)(3/4)

(r1)^3=(21*21*21)/(2*2*2)

r1=21/2 cm

- Radius of the sphere is 21/2 cm.

So, the diameter of the sphere is

(2)(21/2)=21cm.