Jeśli jeden z boków a = 12 cm, to drugi ma

$2\cdot 12+2\cdot b=40$

$2b+24=40\mid -24$

$2b=16\mid :2$    

$b=8\text{cm}$  

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Przypadek I. Gdy h = a.

Mamy

$h=12\text{cm}$

$2r=b=8$

$r=4\text{cm}$

Obliczmy

$P=2\pi r^2+2\pi rh=2\pi \cdot 4^2+2\pi \cdot 4\cdot 12=32\pi +96\pi =128\pi {\text{cm}}^2$

$V=\pi r^2\cdot h=\pi \cdot 4^2\cdot 12=192\pi {\text{cm}}^3$

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Przypadek II. Gdy h = b.

Mamy

$h=8\text{cm}$

$2r=b=12$

$r=6\text{cm}$

Obliczmy

$P=2\pi r^2+2\pi rh=2\pi \cdot 6^2+2\pi \cdot 6\cdot 8=72\pi +96\pi =168\pi {\text{cm}}^2$

$V=\pi r^2\cdot h=\pi \cdot 6^2\cdot 8=288\pi {\text{cm}}^3$