Calculate the volume of a frustum using the given radii and heights.

Urefu wa frustum ($h_{frustum}$) ni tofauti kati ya urefu wa koni kubwa na urefu wa koni ndogo.

$$h_{frustum} = H - h = 25 - 5 = 20$$

Fomula ya ujazo wa frustum ni:

$$V = \frac{1}{3} \pi h_{frustum} (R^2 + Rr + r^2)$$

$$V = \frac{1}{3} \pi (20) (65^2 + 65 \cdot 13 + 13^2)$$ $$V = \frac{20}{3} \pi (4225 + 845 + 169)$$ $$V = \frac{20}{3} \pi (5239)$$ $$V = \boxed{\frac{104780}{3} \pi}$$

Safu ya 2:
Radius kubwa ($R$) = 30
Urefu wa koni kubwa ($H$) = 60
Urefu wa koni ndogo ($h$) = 6

Tumia uwiano wa radius kwa urefu: $\frac{R}{H} = \frac{r}{h}$.

$$\frac{30}{60} = \frac{r}{6}$$ $$r = \frac{30 \times 6}{60} = \frac{180}{60} = 3$$

Radius ndogo iliyokosekana ni $\boxed{3}$.

$$V = \frac{1}{3} \pi (54) (30^2 + 30 \cdot 3 + 3^2)$$ $$V = 18 \pi (900 + 90 + 9)$$ $$V = 18 \pi (999)$$ $$V = \boxed{17982 \pi}$$

Safu ya 3:
Radius kubwa ($R$) = 140
Radius ndogo ($r$) = 21
Urefu wa koni kubwa ($H$) = 56

Tumia uwiano wa radius kwa urefu: $\frac{R}{H} = \frac{r}{h}$.

$$\frac{140}{56} = \frac{21}{h}$$ $$h = \frac{21 \times 56}{140} = \frac{1176}{140} = 8.4$$

Urefu wa koni ndogo uliokosekana ni $\boxed{8.4}$.

$$V = \frac{1}{3} \pi (47.6) (140^2 + 140 \cdot 21 + 21^2)$$ $$V = \frac{47.6}{3} \pi (19600 + 2940 + 441)$$ $$V = \frac{47.6}{3} \pi (22981)$$ $$V = \boxed{\frac{1093307.6}{3} \pi}$$

Safu ya 4:
Radius ndogo ($r$) = 18
Urefu wa koni kubwa ($H$) = 120
Urefu wa koni ndogo ($h$) = 40

Tumia uwiano wa radius kwa urefu: $\frac{R}{H} = \frac{r}{h}$.

$$\frac{R}{120} = \frac{18}{40}$$ $$R = \frac{18 \times 120}{40} = 18 \times 3 = 54$$

Radius kubwa iliyokosekana ni $\boxed{54}$.

$$V = \frac{1}{3} \pi (80) (54^2 + 54 \cdot 18 + 18^2)$$ $$V = \frac{80}{3} \pi (2916 + 972 + 324)$$ $$V = \frac{80}{3} \pi (4212)$$ $$V = 80 \pi (1404)$$ $$V = \boxed{112320 \pi}$$