Approximate percentage increase in the volume of sphere if its radius…

The correct answer is Option (2) → 9%

The volume of a sphere of radius r is

    \( \displaystyle V = \frac{4}{3}\pi r^3 \)

For a small change \(\Delta r\), the approximate change in V is given by the derivative:

    \( \displaystyle \Delta V \approx \frac{dV}{dr}\,\Delta r = 4\pi r^2\,\Delta r \)

Dividing by V:

    \( \displaystyle \frac{\Delta V}{V} \approx \frac{4\pi r^2\,\Delta r}{\frac{4}{3}\pi r^3} = 3\,\frac{\Delta r}{r} \)

The radius increases by 3%, so \(\frac{\Delta r}{r}\times 100 = 3\):

    \( \displaystyle \frac{\Delta V}{V}\times 100 \approx 3 \times 3 = 9 \)

The volume increases by about 9%.

Note: This topic was not in the CUET 2026 syllabus.