Cylinder diameter

The surface of the cylinder is 112 cm2. The cylinder height is 5 cm. What is the diameter of this cylinder?

Correct answer:

D =  4.813 cm

Step-by-step explanation:

S=112 cm2 h=5 cm  S = 2 π r2 + 2 π r h S = π D2/2 + π D h  pi⋅ D2/2+pi⋅ D⋅ h−S=0  3.1415926⋅ D2/2+3.1415926⋅ D⋅ 5−112=0 1.5707963D2+15.708D−112=0  a=1.570796;b=15.708;c=−112 D=b2−4ac=15.7082−4⋅1.570796⋅(−112)=950.4568440094=4.813 cm D>0  D1,2​=2a−b±D​​=3.141593−15.71±950.46​​ D1,2​=−5±9.813328 D1​=4.813328473 D2​=−14.813328473  D>0  D=D1​=4.8133≐4.8133   Verifying Solution:  r=D/2=4.8133/2≐2.4067 cm  S2​=2π⋅ r2+2π⋅ r⋅ h=2⋅ 3.1416⋅ 2.40672+2⋅ 3.1416⋅ 2.4067⋅ 5=112 cm2 S2​=S

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