Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.

Correct result:

h =  24.001 m

Solution:

S=7697 m2 D1=56 m D2=42 m r1=D1/2=56/2=28 m r2=D2/2=42/2=21 m S1=π⋅ r12=3.1416⋅ 282≐2463.0086 m2 S2=π⋅ r22=3.1416⋅ 212≐1385.4424 m2 S3=S−S1−S2=7697−2463.0086−1385.4424≐3848.549 m2 s=S3/π/(r1+r2)=3848.549/3.1416/(28+21)≐25.0006 m h=s2−(r1−r2)2=25.00062−(28−21)2=24.001 mS=7697 \ \text{m}^2 \ \\ D_{1}=56 \ \text{m} \ \\ D_{2}=42 \ \text{m} \ \\ r_{1}=D_{1}/2=56/2=28 \ \text{m} \ \\ r_{2}=D_{2}/2=42/2=21 \ \text{m} \ \\ S_{1}=\pi \cdot \ r_{1}^2=3.1416 \cdot \ 28^2 \doteq 2463.0086 \ \text{m}^2 \ \\ S_{2}=\pi \cdot \ r_{2}^2=3.1416 \cdot \ 21^2 \doteq 1385.4424 \ \text{m}^2 \ \\ S_{3}=S - S_{1}-S_{2}=7697 - 2463.0086-1385.4424 \doteq 3848.549 \ \text{m}^2 \ \\ s=S_{3}/\pi/(r_{1}+r_{2})=3848.549/3.1416/(28+21) \doteq 25.0006 \ \text{m} \ \\ h=\sqrt{ s^2-(r_{1}-r_{2})^2 }=\sqrt{ 25.0006^2-(28-21)^2 }=24.001 \ \text{m}

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