The volume and the radius of both cone and sphere are equal, then find the…
2024
The volume and the radius of both cone and sphere are equal, then find the ratio of height of the cone to the diameter of the sphere?
- A.
2 : 3
- B.
3 : 2
- C.
2 : 1
- D.
1 : 2
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Key steps: Equate volumes and solve for the ratio.
Volume of cone = (1/3)πr^2h, where r is the cone's radius.
Volume of sphere = (4/3)πr^3, using the same radius r (given equal radii).
Set equal: (1/3)πr^2h = (4/3)πr^3. Cancel (1/3)π and r^2 (r>0) to get h = 4r.
Sphere diameter D = 2r. Therefore h : D = 4r : 2r = 2 : 1.
Answer: 2 : 1