A cone is inscribed in a sphere such that the radius of the cone is the same…
2026
A cone is inscribed in a sphere such that the radius of the cone is the same as the radius of the sphere, and the height of the cone is equal to the diameter of the sphere. What is the relationship between the volume of the sphere and the volume of the cone?
- A.
Volume of cone is one-third of volume of sphere.
- B.
Volume of sphere is twice of volume of cone.
- C.
Volume of cone is three-fourth of volume of sphere.
- D.
Volume of cone is two-third of volume of sphere.
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Step 1: Define dimensions.
Let the radius of the sphere be r.
Cone radius = r.
Cone height = Diameter of sphere = 2r.
Step 2: Calculate volumes.
Volume of Sphere = (4/3) × π × r³
Volume of Cone = (1/3) × π × r² × h = (1/3) × π × r² × (2r) = (2/3) × π × r³
Step 3: Compare the volumes.
Ratio: Sphere Volume / Cone Volume = [(4/3)πr³] / [(2/3)πr³] = 4/2 = 2.
Thus, the Volume of the Sphere is twice the Volume of the Cone.
Final Answer: Option 2