Wax cylinder of diameter 21 cm and height 21 cm is chipped off and shaped to form a cone of maximum volume. The chipped off way is recast into a solid sphere. Find the diameter of the sphere.
Answers
Answer:
21
Step-by-step explanation:
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
r^2h=1/3r^2h+4/3(1)^3
r^2h=1/3r^2h+4/3(11)^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.