Shell area cy

The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.

Correct result:

V =  596.831 cm3

Solution:

S=300 cm2 h=12 cm  S=2π⋅ r⋅ h  r=S2π⋅ h=3002⋅ 3.1416⋅ 12≐3.9789 cm S1=π⋅ r2=3.1416⋅ 3.97892≐49.7359 cm2  V=S1⋅ h=49.7359⋅ 12=596.831 cm3S=300 \ \text{cm}^2 \ \\ h=12 \ \text{cm} \ \\ \ \\ S=2 \pi \cdot \ r \cdot \ h \ \\ \ \\ r=\dfrac{ S }{ 2 \pi \cdot \ h }=\dfrac{ 300 }{ 2 \cdot \ 3.1416 \cdot \ 12 } \doteq 3.9789 \ \text{cm} \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 3.9789^2 \doteq 49.7359 \ \text{cm}^2 \ \\ \ \\ V=S_{1} \cdot \ h=49.7359 \cdot \ 12=596.831 \ \text{cm}^3

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