Koliko iznosi polumjer kugle dobivene pretapanjem metalne kocke brida duljine $5 \text{ cm}$$5 \text{ cm}$?

Izjednačavamo volumen kocke i volumen kugle.
1. Volumen kocke s bridom $a=5$$a=5$: $V_{kocke} = a^3 = 5^3 = 125$$V_{kocke} = a^3 = 5^3 = 125$.
2. Volumen kugle: $V_{kugle} = \frac{4}{3}r^3\pi$$V_{kugle} = \frac{4}{3}r^3\pi$.
3. Izjednačimo i riješimo po $r$$r$:
$\frac{4}{3}r^3\pi = 125 \quad /\cdot 3$$\frac{4}{3}r^3\pi = 125 \quad /\cdot 3$
$4r^3\pi = 375 \quad /:4\pi$$4r^3\pi = 375 \quad /:4\pi$
$r^3 = \frac{375}{4\pi}$$r^3 = \frac{375}{4\pi}$
$r = \sqrt[3]{\frac{375}{4\pi}} \approx 3.10$$r = \sqrt[3]{\frac{375}{4\pi}} \approx 3.10$ cm.
Odgovor: C