Question

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.

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Answer 1

${\bf{\underline{\underline \blue{ Answer }}}}$

• Height of cylinder/cone (h)= 24cm
• Radius of cylinder/cone (r)= 7cm

${\bf{\underline{\underline \purple{ To\:Find }}}}$

• We have to find out the Volume and surface area of remaining solid

${\bf{\underline{\underline \blue{ Solution }}}}$

Volume of remaining solid = Volume of cylinder- Volume of cone

$:\implies\sf\ V.\ of\ remaining\ solid = \pi r^2 h-\dfrac{1}{3}\pi r^2\ h \\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid = \dfrac{1}{3}\pi r^2 h\big(3-1\big)\\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid = \dfrac{1}{\cancel3}\times \dfrac{22}{\cancel{7}}\times \cancel{7}\times 7\times \cancel{24}\times \big(2\big)\\ \\ \\ :\implies\sf\ V.\ of\ remaining\ solid =22\times 7\times 8\times 2\\ \\ \\ :\implies\underline{\boxed{\blue{\sf\ Volume\ of\ remaining\ solid = 2624cm^3}}}$

● Surface area of remaining solid = CSA of cylinder+ CSA of cone + Area of top (circular part)

$\sf\bigstar\ \ Surface\ Area= 2\pi r h+ \pi r \ell + \pi r^2$

$\bullet\sf \ell= \sqrt{r^2+h^2}\\ \\ \longmapsto\sf \ell= \sqrt{(7)^2+(24)^2}\\ \\ \longmapsto\sf \ell= \sqrt{49+576}\\ \\ \longmapsto\sf \ell= \sqrt{625}\\ \\ \underline{\boxed{\sf\ \ell= 25cm}}$

Now surface Area :-

$:\implies\sf\ Surface\ Area= \pi r\big\lgroup 2h+\ell+r\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= \dfrac{22}{\cancel{7}}\times \cancel{7}\big\lgroup (2\times 24)+ 25+7\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= 22\times \big\lgroup 48+32\big\rgroup\\ \\ \\ :\implies\sf\ Surface\ Area= 22\times 80\\ \\ \\ :\implies\underline{\boxed{\purple{\sf\ Surface\ area\ of\ remaining\ solid= 1760cm^2}}}$

Answer 2

Answer:

pls see the attachment

Step-by-step explanation:

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