The masses of two similar solid cylinders are 4752 g and 1408 g. If the difference in area of the curved surfaces of the two cylinders is 280 cm², find the area of the curved surface of the larger cylinder.

Kwa mitungi miwili inayofanana, uwiano wa masi zao ni sawa na uwiano wa ujazo wao, ambao ni mchemraba wa uwiano wa vipimo vyao vya urefu.
Tutaweka $M_1$ kuwa masi ya silinda kubwa na $M_2$ kuwa masi ya silinda ndogo.

$$\frac{M_1}{M_2} = \frac{4752 \text{ g}}{1408 \text{ g}} = 3.375$$

Ikiwa uwiano wa masi ni $\left(\frac{L_1}{L_2}\right)^3$, basi:

$$\left(\frac{L_1}{L_2}\right)^3 = 3.375$$

Chukua mzizi wa tatu (cube root) pande zote mbili:

$$\frac{L_1}{L_2} = \sqrt[3]{3.375} = 1.5$$

Kwa mitungi inayofanana, uwiano wa eneo la nyuso zao ni sawa na mraba wa uwiano wa vipimo vyao vya urefu.
Tutaweka $A_1$ kuwa eneo la uso uliopinda wa silinda kubwa na $A_2$ kuwa eneo la uso uliopinda wa silinda ndogo.

$$\frac{A_1}{A_2} = \left(\frac{L_1}{L_2}\right)^2 = (1.5)^2 = 2.25$$

Hii inamaanisha $A_1 = 2.25 A_2$.

Tunajua tofauti ya eneo la nyuso zilizopinda ni 280 cm$^2$:

$$A_1 - A_2 = 280 \text{ cm}^2$$

Badilisha $A_1 = 2.25 A_2$ kwenye mlinganyo huu:

$$2.25 A_2 - A_2 = 280 \text{ cm}^2$$ $$1.25 A_2 = 280 \text{ cm}^2$$ $$A_2 = \frac{280}{1.25} \text{ cm}^2 = 224 \text{ cm}^2$$

Sasa tafuta $A_1$:

$$A_1 = 2.25 \times A_2 = 2.25 \times 224 \text{ cm}^2 = 504 \text{ cm}^2$$

Eneo la uso uliopinda wa silinda kubwa ni $\text{504 cm}^2$.