From a right circular cylinder of radius 7 cm, height 24cm of conical cavity of same base radius and of same height hollowed out. find the volume and whole surface of remaining solid. spammers stay away…. About the author Liliana
Answer: pls see the attachment Step-by-step explanation: hope it help uh freind Mark me brainliest Reply
[tex]{\bf{\underline{\underline \blue{ Answer }}}}[/tex] Height of cylinder/cone (h)= 24cm Radius of cylinder/cone (r)= 7cm [tex]{\bf{\underline{\underline \purple{ To\:Find }}}}[/tex] We have to find out the Volume and surface area of remaining solid [tex]{\bf{\underline{\underline \blue{ Solution }}}}[/tex] Volume of remaining solid = Volume of cylinder- Volume of cone [tex]:\implies\sf\ V.\ of\ remaining\ solid = \pi r^2 h-\dfrac{1}{3}\pi r^2\ h \\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid = \dfrac{1}{3}\pi r^2 h\big(3-1\big)\\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid = \dfrac{1}{\cancel3}\times \dfrac{22}{\cancel{7}}\times \cancel{7}\times 7\times \cancel{24}\times \big(2\big)\\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid =22\times 7\times 8\times 2\\ \\ \\ :\implies\underline{\boxed{\blue{\sf\ Volume\ of\ remaining\ solid = 2624cm^3}}}[/tex] ● Surface area of remaining solid = CSA of cylinder+ CSA of cone + Area of top (circular part) [tex]\sf\bigstar\ \ Surface\ Area= 2\pi r h+ \pi r \ell + \pi r^2[/tex] [tex]\bullet\sf \ell= \sqrt{r^2+h^2}\\ \\ \longmapsto\sf \ell= \sqrt{(7)^2+(24)^2}\\ \\ \longmapsto\sf \ell= \sqrt{49+576}\\ \\ \longmapsto\sf \ell= \sqrt{625}\\ \\ \underline{\boxed{\sf\ \ell= 25cm}}[/tex] Now surface Area :- [tex]:\implies\sf\ Surface\ Area= \pi r\big\lgroup 2h+\ell+r\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= \dfrac{22}{\cancel{7}}\times \cancel{7}\big\lgroup (2\times 24)+ 25+7\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= 22\times \big\lgroup 48+32\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= 22\times 80\\ \\ \\ :\implies\underline{\boxed{\purple{\sf\ Surface\ area\ of\ remaining\ solid= 1760cm^2}}}[/tex] Reply
Answer:
pls see the attachment
Step-by-step explanation:
hope it help uh freind Mark me brainliest
[tex]{\bf{\underline{\underline \blue{ Answer }}}}[/tex]
[tex]{\bf{\underline{\underline \purple{ To\:Find }}}}[/tex]
[tex]{\bf{\underline{\underline \blue{ Solution }}}}[/tex]
Volume of remaining solid = Volume of cylinder- Volume of cone
[tex]:\implies\sf\ V.\ of\ remaining\ solid = \pi r^2 h-\dfrac{1}{3}\pi r^2\ h \\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid = \dfrac{1}{3}\pi r^2 h\big(3-1\big)\\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid = \dfrac{1}{\cancel3}\times \dfrac{22}{\cancel{7}}\times \cancel{7}\times 7\times \cancel{24}\times \big(2\big)\\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid =22\times 7\times 8\times 2\\ \\ \\ :\implies\underline{\boxed{\blue{\sf\ Volume\ of\ remaining\ solid = 2624cm^3}}}[/tex]
● Surface area of remaining solid = CSA of cylinder+ CSA of cone + Area of top (circular part)
[tex]\sf\bigstar\ \ Surface\ Area= 2\pi r h+ \pi r \ell + \pi r^2[/tex]
[tex]\bullet\sf \ell= \sqrt{r^2+h^2}\\ \\ \longmapsto\sf \ell= \sqrt{(7)^2+(24)^2}\\ \\ \longmapsto\sf \ell= \sqrt{49+576}\\ \\ \longmapsto\sf \ell= \sqrt{625}\\ \\ \underline{\boxed{\sf\ \ell= 25cm}}[/tex]
Now surface Area :-
[tex]:\implies\sf\ Surface\ Area= \pi r\big\lgroup 2h+\ell+r\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= \dfrac{22}{\cancel{7}}\times \cancel{7}\big\lgroup (2\times 24)+ 25+7\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= 22\times \big\lgroup 48+32\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= 22\times 80\\ \\ \\ :\implies\underline{\boxed{\purple{\sf\ Surface\ area\ of\ remaining\ solid= 1760cm^2}}}[/tex]