Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 204310 by BaliramKumar last updated on 12/Feb/24

Answered by mr W last updated on 12/Feb/24

Commented by mr W last updated on 12/Feb/24

R=(3/2) OT=5 OA=(√(5^2 −((3/2))^2 ))=((√(91))/2) (r/R)=((OA)/(OT)) ⇒r=((√(91))/(2×5))×(3/2)=((3(√(91)))/(20)) h=R−(√(R^2 −r^2 ))=(3/2)−(√(((3/2))^2 −(((3(√(91)))/(20)))^2 ))=((21)/(20)) A_(cap) =2πRh=2π×(3/2)×((21)/(20))=((63π)/(20)) ✓

$${R}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${OT}=\mathrm{5} \\ $$$${OA}=\sqrt{\mathrm{5}^{\mathrm{2}} −\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} }=\frac{\sqrt{\mathrm{91}}}{\mathrm{2}} \\ $$$$\frac{{r}}{{R}}=\frac{{OA}}{{OT}} \\ $$$$\Rightarrow{r}=\frac{\sqrt{\mathrm{91}}}{\mathrm{2}×\mathrm{5}}×\frac{\mathrm{3}}{\mathrm{2}}=\frac{\mathrm{3}\sqrt{\mathrm{91}}}{\mathrm{20}} \\ $$$${h}={R}−\sqrt{{R}^{\mathrm{2}} −{r}^{\mathrm{2}} }=\frac{\mathrm{3}}{\mathrm{2}}−\sqrt{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{3}\sqrt{\mathrm{91}}}{\mathrm{20}}\right)^{\mathrm{2}} }=\frac{\mathrm{21}}{\mathrm{20}} \\ $$$${A}_{{cap}} =\mathrm{2}\pi{Rh}=\mathrm{2}\pi×\frac{\mathrm{3}}{\mathrm{2}}×\frac{\mathrm{21}}{\mathrm{20}}=\frac{\mathrm{63}\pi}{\mathrm{20}}\:\checkmark \\ $$

Commented by mr W last updated on 12/Feb/24

Commented by BaliramKumar last updated on 12/Feb/24

thanks 🙏🙏🙏🙏🙏

$$\mathrm{thanks}\: \\ $$🙏🙏🙏🙏🙏

Terms of Service

Privacy Policy

Contact: info@tinkutara.com