Question-158209

Question Number 158209 by cortano last updated on 01/Nov/21

Answered by mr W last updated on 01/Nov/21

Commented by Rasheed.Sindhi last updated on 01/Nov/21

$${Mr}\:{cortano},\:{You}\:{should}\:{give}\:{more} \\ $$$${feedback}\:{than}\:{merely}\:'{yes}'.{Sir} \\ $$$${mr}\:{W}\:{has}\:{done}\:{a}\:{lot}\:{of}\:{labour}\:{for} \\ $$$${you}.{He}\:{has}\:{drawn}\:{a}\:{nice}\:\:{picture} \\ $$$${to}\:{make}\:{you}\:{understand}!\:{His}\:{answer} \\ $$$${is}\:{creative}.{You}\:{should}\:{have}\:{paid} \\ $$$$\boldsymbol{{at}}\:\boldsymbol{{least}}\:{thanks}\:{to}\:{him}. \\ $$$${Sorry}\:{if}\:{my}\:{words}\:{hurt}\:{you}. \\ $$

Commented by mr W last updated on 01/Nov/21

y_P =2×4=8 x_P =(4/( (√3))) V_R =2π×((2×4×4)/(3×(√3)))×((3×4)/(8×(√3))) ⇒V_R =((32π)/3) V_S =2π[((8×4)/(2×(√3)))×((2×8)/3)−((2×4×4)/(3×(√3)))×(4+((3×4)/5))] ⇒V_S =((512π)/(15(√3))) (V_S /V_R )=((512π)/(15(√3)))×(3/(32π))=((16(√3))/(15))

$${y}_{{P}} =\mathrm{2}×\mathrm{4}=\mathrm{8} \\ $$$${x}_{{P}} =\frac{\mathrm{4}}{\:\sqrt{\mathrm{3}}} \\ $$$${V}_{{R}} =\mathrm{2}\pi×\frac{\mathrm{2}×\mathrm{4}×\mathrm{4}}{\mathrm{3}×\sqrt{\mathrm{3}}}×\frac{\mathrm{3}×\mathrm{4}}{\mathrm{8}×\sqrt{\mathrm{3}}} \\ $$$$\Rightarrow{V}_{{R}} =\frac{\mathrm{32}\pi}{\mathrm{3}} \\ $$$${V}_{{S}} =\mathrm{2}\pi\left[\frac{\mathrm{8}×\mathrm{4}}{\mathrm{2}×\sqrt{\mathrm{3}}}×\frac{\mathrm{2}×\mathrm{8}}{\mathrm{3}}−\frac{\mathrm{2}×\mathrm{4}×\mathrm{4}}{\mathrm{3}×\sqrt{\mathrm{3}}}×\left(\mathrm{4}+\frac{\mathrm{3}×\mathrm{4}}{\mathrm{5}}\right)\right] \\ $$$$\Rightarrow{V}_{{S}} =\frac{\mathrm{512}\pi}{\mathrm{15}\sqrt{\mathrm{3}}} \\ $$$$\frac{{V}_{{S}} }{{V}_{{R}} }=\frac{\mathrm{512}\pi}{\mathrm{15}\sqrt{\mathrm{3}}}×\frac{\mathrm{3}}{\mathrm{32}\pi}=\frac{\mathrm{16}\sqrt{\mathrm{3}}}{\mathrm{15}} \\ $$

Commented by cortano last updated on 01/Nov/21