Given below is a rectangular container without a cover whose total surface area is 111cm². Find the length of the container.

Kontena ni mstatili (cuboid) na vipimo vifuatavyo:

• Upana ($w$) = $3 \text{ cm}$
• Kimo ($h$) = $6 \text{ cm}$
• Urefu ($l$) = $y \text{ cm}$ (tunahitaji kupata hii)

Kwa kuwa kontena haina kifuniko, ina nyuso 5: chini, mbele, nyuma, na pande mbili.
Eneo la chini = $l \times w = y \times 3 = 3y \text{ cm}^2$
Eneo la mbele na nyuma = $2 \times (l \times h) = 2 \times (y \times 6) = 12y \text{ cm}^2$
Eneo la pande mbili = $2 \times (w \times h) = 2 \times (3 \times 6) = 2 \times 18 = 36 \text{ cm}^2$

Jumla ya eneo la uso (Total Surface Area, TSA) = Eneo la chini + Eneo la mbele na nyuma + Eneo la pande mbili.

$$\text{TSA} = 3y + 12y + 36$$ $$\text{TSA} = 15y + 36$$

Tunapewa kuwa jumla ya eneo la uso ni $111 \text{ cm}^2$.

$$111 = 15y + 36$$

Toa 36 kutoka pande zote mbili za mlinganyo:

$$111 - 36 = 15y$$ $$75 = 15y$$

Gawanya pande zote mbili kwa 15:

$$y = \frac{75}{15}$$ $$y = 5$$

Kwa hiyo, urefu wa kontena ni $5 \text{ cm}$.