Question

Froma 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 ​

Answer 1

Given :-

Height of cylinder/cone (h)= 24cm

Radius of cylinder/cone (r)= 7cm

To Find :-

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

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

Given :-

From a right circular cylinder of radius 7 cm, height 24cm of conical cavity of same base radius and of same height hollowed out.

To Find :-

Volume remaining

total surface

Solution :-

Here, volume of remaining solid

=>$\sf V = \dfrac{1}{3} \pi r^{2} h (3 - 1)$

=> V = 1/3 * 22/7 * 7 * 7 * 24 (2)

=> V = 1/3 * 22 * 7 * 24 (2)

=> V = 1 * 22 * 7 * 8 * 2

=> V = 22 * 7 * 16

=> V = 2464 cm

Now,

we know that

$\sf Slangth \; height^{2} = Radius^{2} + Height^{2}$

$\sf l^{2} = 24^{2} + 7^{2}$

$\sf l^{2} = 625$

l = 25 cm

$\sf SA = 2\pi r h + \pi r^{2} + \pi rl$

$\sf SA = 2 \times \dfrac{22}7 \times 7 \times 24 + \dfrac{22}7 \times 7^{2} + \dfrac{22}7 \times 7 \times 25$

SA = 2 * 22 * 24 + 22/7 * 49 + 22 * 25

SA = 44 * 24 + 22 * 7 + 22 * 25

SA = 1320 CM