Sphere: Surface Area and Volume

A sphere of radius r has surface area $S = 4\pi r^2$ and volume $V = \frac{4}{3}\pi r^3$. The surface grows as $r^2$ while the volume grows much faster as $r^3$, which is why bigger balls feel disproportionately heavier.

Slide r and watch S and V update side by side. Try r = 7 to see surface roughly 615.75 and volume roughly 1436.76. Doubling r multiplies surface by 4 and volume by 8.

Students forget the $\frac{4}{3}$ in the volume or use $r^2$ instead of $r^3$. Also, many confuse surface area with cross-section area $\pi r^2$. Write the formula first, then substitute.

Cricket balls, laddoos and water tanks are roughly spherical. A spherical water tank of radius 1 m holds about 4188 litres, much more than a cubical tank of side 1 m at 1000 litres. The lab quickly shows this scaling.