Question

If the radius of a sphere is tripled, then its volume will become

• A. 27 times
• B. 9 times
• C. \(\frac{1}{3}\) times
• D. double

Answer 1

The Correct Option is A

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

The volume \( V \) of a sphere is given by:

\[ V = \frac{4}{3} \pi r^3, \]

where \( r \) is the radius of the sphere.

Step 2: Analyze the effect of tripling the radius.

If the radius is tripled, the new radius becomes \( 3r \). Substituting \( 3r \) into the formula for the volume:

\[ V_{\text{new}} = \frac{4}{3} \pi (3r)^3. \]

Simplify the expression:

\[ V_{\text{new}} = \frac{4}{3} \pi (27r^3) = 27 \cdot \frac{4}{3} \pi r^3 = 27 \cdot V. \]

Step 3: Conclude the result.

When the radius of a sphere is tripled, its volume increases by a factor of \( 27 \).

Final Answer: The volume of the sphere will become \( \mathbf{27 \text{ times}} \) its original volume.