Volume Of A Sphere

Let the radius of the sphere be , and the radius of the cone be , with their volumes being equal. The volume of a sphere is given by: The volume of a cone is given by: where is the height of the cone, and we are given that the diameter of the sphere is equal to the height of the cone, so . Now, equating the two volumes since the volumes are equal: Simplifying this: Canceling out from both sides: Dividing both sides by 2:

The correct answer is option (A):

Step 1: Recall the formula for the volume of a sphere.

The volume of a sphere is given by:

where is the radius of the sphere.

Step 2: Analyze the effect of tripling the radius.

If the radius is tripled, the new radius becomes . Substituting into the formula for the volume:

Simplify the expression:

Step 3: Conclude the result.

When the radius of a sphere is tripled, its volume increases by a factor of .

Final Answer: The volume of the sphere will become its original volume.

Correct answer:

Explanation:
The formula for the volume of a sphere is: where is the radius of the sphere. The diameter is related to the radius by: Substituting this into the volume formula:

Hence, the volume of the sphere is .