Question-220208

Question Number 220208 by Tawa11 last updated on 08/May/25

Commented by Tawa11 last updated on 08/May/25

Find the volume and area of the shape. volume = (1/2)πr^2 h but I am not getting the area. What is the area please?

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{and}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{shape}. \\ $$$$\mathrm{volume}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\pi\mathrm{r}^{\mathrm{2}} \mathrm{h}\:\:\:\:\:\mathrm{but}\:\mathrm{I}\:\mathrm{am}\:\mathrm{not}\:\mathrm{getting}\:\mathrm{the}\:\mathrm{area}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{please}? \\ $$

Commented by fantastic last updated on 08/May/25

Answered by mr W last updated on 08/May/25

Commented by mr W last updated on 08/May/25

r=(7/2)=3.5, h=13 total surface area S = (1)+2×(2)+(3) (1)=rectangle=2rh (2)=semi−circle=((πr^2 )/2) (3)=half of cylinder=πrh ⇒S=2rh+2×((πr^2 )/2)+πrh =(2+π)rh+πr^2 =(2+π)×3.5×13+π×3.5^2 ≈272.43

$${r}=\frac{\mathrm{7}}{\mathrm{2}}=\mathrm{3}.\mathrm{5},\:{h}=\mathrm{13} \\ $$$${total}\:{surface}\:{area}\:{S}\:=\:\left(\mathrm{1}\right)+\mathrm{2}×\left(\mathrm{2}\right)+\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{1}\right)={rectangle}=\mathrm{2}{rh} \\ $$$$\left(\mathrm{2}\right)={semi}−{circle}=\frac{\pi{r}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)={half}\:{of}\:{cylinder}=\pi{rh} \\ $$$$\Rightarrow{S}=\mathrm{2}{rh}+\mathrm{2}×\frac{\pi{r}^{\mathrm{2}} }{\mathrm{2}}+\pi{rh} \\ $$$$\:\:\:\:=\left(\mathrm{2}+\pi\right){rh}+\pi{r}^{\mathrm{2}} \\ $$$$\:\:\:\:=\left(\mathrm{2}+\pi\right)×\mathrm{3}.\mathrm{5}×\mathrm{13}+\pi×\mathrm{3}.\mathrm{5}^{\mathrm{2}} \approx\mathrm{272}.\mathrm{43} \\ $$

Commented by Tawa11 last updated on 08/May/25

$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}. \\ $$

Answered by MathematicalUser2357 last updated on 08/May/25

πr(r+h)+2rh Ans: π∙3.5(3.5+13)+2∙3.5∙13=(57.75π+91)u^2 determinant ((( 57.75)),(( ×3.1415)),(( 28875)),(( 5775×)),(( 23100××)),(( 5775×××)),((17325××××)),((181.421625))) Or 272.421625u^2

$$\pi{r}\left({r}+{h}\right)+\mathrm{2}{rh} \\ $$$$\mathrm{Ans}:\:\pi\centerdot\mathrm{3}.\mathrm{5}\left(\mathrm{3}.\mathrm{5}+\mathrm{13}\right)+\mathrm{2}\centerdot\mathrm{3}.\mathrm{5}\centerdot\mathrm{13}=\left(\mathrm{57}.\mathrm{75}\pi+\mathrm{91}\right){u}^{\mathrm{2}} \\ $$$$\begin{array}{|c|c|c|c|c|c|c|c|}{\:\:\:\:\:\mathrm{57}.\mathrm{75}}\\{\:\:\:×\mathrm{3}.\mathrm{1415}}\\{\:\:\:\:\mathrm{28875}}\\{\:\:\:\:\mathrm{5775}×}\\{\:\:\mathrm{23100}××}\\{\:\:\mathrm{5775}×××}\\{\mathrm{17325}××××}\\{\mathrm{181}.\mathrm{421625}}\\\hline\end{array} \\ $$$$\mathrm{Or}\:\mathrm{272}.\mathrm{421625}{u}^{\mathrm{2}} \\ $$

Commented by Tawa11 last updated on 08/May/25

$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}. \\ $$

Answered by fantastic last updated on 08/May/25

area of the rectangle of opposite side a_1 =7×13 =91u^2 area of the two half circles a_2 =2((1/2)πr^2 )=πr^2 u^2 =π(3.5)^2 u^2 =12.25π u^2 length of ⌢_(acb) =πr u ∴area of the curved part=a_3 =πr×13 u^2 =π×3.5×13=45.5π u^2 total area =a_1 +a_2 +a_3 =(91+12.25π+45.5π)u^2 ≈272.426975744811

$${area}\:{of}\:{the}\:{rectangle}\:{of}\:{opposite}\:{side} \\ $$$${a}_{\mathrm{1}} =\mathrm{7}×\mathrm{13}\:=\mathrm{91}{u}^{\mathrm{2}} \\ $$$${area}\:{of}\:{the}\:{two}\:{half}\:{circles} \\ $$$${a}_{\mathrm{2}} =\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}\pi{r}^{\mathrm{2}} \right)=\pi{r}^{\mathrm{2}} {u}^{\mathrm{2}} =\pi\left(\mathrm{3}.\mathrm{5}\right)^{\mathrm{2}} {u}^{\mathrm{2}} =\mathrm{12}.\mathrm{25}\pi\:{u}^{\mathrm{2}} \\ $$$${length}\:{of}\:\underset{{acb}} {\frown}=\pi{r}\:{u}\: \\ $$$$\therefore{area}\:{of}\:{the}\:{curved}\:{part}={a}_{\mathrm{3}} =\pi{r}×\mathrm{13}\:{u}^{\mathrm{2}} =\pi×\mathrm{3}.\mathrm{5}×\mathrm{13}=\mathrm{45}.\mathrm{5}\pi\:{u}^{\mathrm{2}} \\ $$$$\boldsymbol{{total}}\:\boldsymbol{{area}}\:=\boldsymbol{{a}}_{\mathrm{1}} +\boldsymbol{{a}}_{\mathrm{2}} +\boldsymbol{{a}}_{\mathrm{3}} =\left(\mathrm{91}+\mathrm{12}.\mathrm{25}\pi+\mathrm{45}.\mathrm{5}\pi\right){u}^{\mathrm{2}} \\ $$$$\approx\mathrm{272}.\mathrm{426975744811} \\ $$

Commented by Tawa11 last updated on 08/May/25

$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{appreciate}. \\ $$

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