Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.

Result

V =  2.548 dm3
S =  33.567 dm2

Solution:

r=2.3 dm v=46/100=2350=0.46 dm S1=π r2=3.1416 2.3216.619 dm2 V=S1 v/3=16.619 0.46/32.54832.548 dm3r=2.3 \ \text{dm} \ \\ v=46/100=\dfrac{ 23 }{ 50 }=0.46 \ \text{dm} \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 2.3^2 \doteq 16.619 \ \text{dm}^2 \ \\ V=S_{1} \cdot \ v/3=16.619 \cdot \ 0.46/3 \doteq 2.5483 \doteq 2.548 \ \text{dm}^3
 s=r2+v2=2.32+0.4622.3455 dm S2=π r s=3.1416 2.3 2.345516.9481 dm2 S=S1+S2=16.619+16.948133.567233.567 dm2 \ \\ s=\sqrt{ r^2+v^2 }=\sqrt{ 2.3^2+0.46^2 } \doteq 2.3455 \ \text{dm} \ \\ S_{2}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 2.3 \cdot \ 2.3455 \doteq 16.9481 \ \text{dm}^2 \ \\ S=S_{1}+S_{2}=16.619+16.9481 \doteq 33.5672 \doteq 33.567 \ \text{dm}^2



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