Rotary cylinder

In the rotary cylinder it is given: surface S = 96 cm2 and volume V = 192 cm cubic. Calculate its radius and height.

Correct answer:

r =  -5.1994 cm
h =  2.2607 cm

Step-by-step explanation:

S=96 cm2 V=192 cm3  S=2π⋅ r2+2π⋅ r⋅ h V=πr2 h  S/(2π)=r2+r⋅ h V/π=r2 h  rh=V/(π⋅ r)  S/(2π)=r2+V/(π⋅ r) S/2=π⋅ r2+V/r r⋅ S/2=π⋅ r3+V  r=−5.1994=−5.1994 cm h=π⋅ r2V​=3.1416⋅ (−5.1994)2192​≐2.2607 cm   Verifying Solution:  S1​=2π⋅ r2+2π⋅ r⋅ h=2⋅ 3.1416⋅ (−5.1994)2+2⋅ 3.1416⋅ (−5.1994)⋅ 2.2607≐96.0035 V1​=π⋅ r2⋅ h=3.1416⋅ (−5.1994)2⋅ 2.2607=192  S1​=S,V1​=V

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