Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 169860 by Shrinava last updated on 11/May/22

y = x^2  + 1  y = 0  x = - 1  x = 2  find the volume of the object obtained  by rotating the figure bounded by lines  around the abscissa axis

$$\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\mathrm{y}\:=\:\mathrm{0} \\ $$$$\mathrm{x}\:=\:-\:\mathrm{1} \\ $$$$\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}\:\mathrm{obtained} \\ $$$$\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{lines} \\ $$$$\mathrm{around}\:\mathrm{the}\:\mathrm{abscissa}\:\mathrm{axis} \\ $$

Answered by mr W last updated on 11/May/22

Commented by mr W last updated on 11/May/22

trying without integral calculation.  V_1 =2π×3×1×0.5=3π  V_2 =2π×((1×1)/3)×(1+(1/4))=((5π)/6)  V_3 =2π×((2×4)/3)×(1+(4/4))=((32π)/3)  ⇒V=Σ=((29π)/2)

$${trying}\:{without}\:{integral}\:{calculation}. \\ $$$${V}_{\mathrm{1}} =\mathrm{2}\pi×\mathrm{3}×\mathrm{1}×\mathrm{0}.\mathrm{5}=\mathrm{3}\pi \\ $$$${V}_{\mathrm{2}} =\mathrm{2}\pi×\frac{\mathrm{1}×\mathrm{1}}{\mathrm{3}}×\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)=\frac{\mathrm{5}\pi}{\mathrm{6}} \\ $$$${V}_{\mathrm{3}} =\mathrm{2}\pi×\frac{\mathrm{2}×\mathrm{4}}{\mathrm{3}}×\left(\mathrm{1}+\frac{\mathrm{4}}{\mathrm{4}}\right)=\frac{\mathrm{32}\pi}{\mathrm{3}} \\ $$$$\Rightarrow{V}=\Sigma=\frac{\mathrm{29}\pi}{\mathrm{2}} \\ $$

Commented by Shrinava last updated on 12/May/22

Perfect dear professor thank you

$$\mathrm{Perfect}\:\mathrm{dear}\:\mathrm{professor}\:\mathrm{thank}\:\mathrm{you} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com