50 Yuzi 144 cm² bo'lgan doira diametrini toping.

Doira yuzining formulasi:

\( A = \pi r^2 \).

Shuningdek, radius diametrning yarimiga teng: \( r = \frac{d}{2} \). Shuning uchun yuz formulasi diametr orqali quyidagicha yozilishi mumkin:

\( A = \frac{\pi d^2}{4} \),

bu yerda \( A \) — doira yuzi, \( \pi \) — son, \( d \) — diametr.

Berilgan:

• Yuzi \( A = 144\pi \text{ sm}^2 \).

Diametrni topish uchun formulani o'zgartiramiz:

\( d^2 = \frac{4A}{\pi} \)

\( d = \sqrt{\frac{4A}{\pi}} \)

Hisoblash:

\( d^2 = \frac{4 \cdot 144\pi \text{ sm}^2}{\pi} \)

\( d^2 = 4 \cdot 144 \text{ sm}^2 \)

\( d^2 = 576 \text{ sm}^2 \)

\( d = \sqrt{576 \text{ sm}^2} \)

\( d = 24 \text{ sm} \)

Ответ: Doira diametri \( 24 \text{ sm} \).