Riješite zadatke.

Računamo oplošje stošca:
1. Izračunamo polumjer baze $r$$r$ pomoću Pitagore ($s=13, v=12$$s=13, v=12$):
$r = \sqrt{13^2 - 12^2} = \sqrt{169 - 144} = \sqrt{25} = 5$$r = \sqrt{13^2 - 12^2} = \sqrt{169 - 144} = \sqrt{25} = 5$ cm
2. Formula za oplošje: $O = r\pi(r+s)$$O = r\pi(r+s)$
$O = 5\pi(5 + 13) = 5\pi(18) = 90\pi$$O = 5\pi(5 + 13) = 5\pi(18) = 90\pi$ cm$^2$$^2$

Računamo volumen kocke:
1. Zadano je da je oplošje kocke ($6a^2$$6a^2$) jednako oplošju kvadra dimenzija 3, 12, 15.
$6a^2 = 2(3\cdot12 + 3\cdot15 + 12\cdot15) = 2(36 + 45 + 180) = 522$$6a^2 = 2(3\cdot12 + 3\cdot15 + 12\cdot15) = 2(36 + 45 + 180) = 522$
2. Izračunamo stranicu $a$$a$:
$a^2 = \frac{522}{6} = 87 \implies a = \sqrt{87}$$a^2 = \frac{522}{6} = 87 \implies a = \sqrt{87}$
3. Volumen kocke: $V = a^3 = (\sqrt{87})^3 = 87\sqrt{87}$$V = a^3 = (\sqrt{87})^3 = 87\sqrt{87}$