Question

The volume of a sphere of radius r is obtained by multiplying its surface area with :

• A. \(\frac{4}{3}\)
• B. \(\frac{r}{3}\)
• C. \(\frac{4r}{3}\)
• D. 3r

Answer 1

The Correct Option is B

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

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

To find out how the volume \(V\) relates to its surface area \(A\), we first write the formula for the sphere's surface area:

\[ A = 4 \pi r^2 \]

Now, if the volume is obtained by multiplying the surface area by some factor, we denote this factor as \(k\), such that:

\[ V = A \times k \]

Substituting the expressions for volume and surface area, we get:

\[ \frac{4}{3} \pi r^3 = 4 \pi r^2 \times k \]

By simplifying this equation, we cancel out \(4 \pi r^2\) from both sides:

\[ \frac{1}{3} r = k \]

Thus, we find:

\[ k = \frac{r}{3} \]

Therefore, the volume of a sphere is obtained by multiplying its surface area by \(\frac{r}{3}\).