Question

Vloume of cylinder 1232 m³ and height is 8 cm . find CSA and TSA .​

Answer 1

Height = 8cm

Volume of cylinder = 1232 m ^ 3

we know that volume of cylinder = πr^2h

so,

1232 = 22/ 7 ✖ r ^ 2 ✖ 8

r^ 2 = 1232 ✖ 8 / 7

r = 7

CSA = 2πrh

so,

2 ✖ 22 / 7 ✖ 7 ✖ 8

so we get 252 cm ^ 2

TSA of cylinder = 2πr ( r + h)

2 ✖ 22 / 7 ✖7 ( 7 + 8 )

2580 cm^ 2

Hope it is helpful

Answer 2

$\sf \pink{Given}\begin{cases}&\sf{Volume\:of\:the\:cylinder\:\bf{1232\:cm^3.}} \\ \\ &\sf{Height\:of\:the\:cylinder\:is\:\bf{8\:cm.}}\end{cases}$

To FinD:-

We have to find the Curved Surface Area and Total Surface Area of the cylinder.

Diagram :

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{r=7\:cm}}\put(9,17.5){\sf{h=8\:cm}}\put(-5,-12.7){\bf{@srijaqueen}}\end{picture}$

We know that if we are given the volume and height of the cylinder we have to find the radius.

• Let the radius be r.

We know that,

$\small{\green{\underline{\boxed{\bf{Volume=\pi\:r^2\:h}}}}}$

where,

• π = 22/7
• h is height = 8 cm
• r is radius = r
• Volume = 1232 cm³

Putting the values,

$\small\implies{\sf{1232=\dfrac{22}{7}\times\:r^2\times8}}$

$\small\implies{\sf{\dfrac{1232\times7}{22\times8}=r^2}}$

$\small\implies{\sf{\dfrac{8624}{176}=r^2}}$

$\small\implies{\sf{\dfrac{\cancel{8624}}{\cancel{176}}=r^2}}$

$\small\implies{\sf{49=r^2}}$

Square rooting both the sides,

$\small\implies{\sf{\sqrt{49}=r}}$

$\small\therefore\boxed{\bf{Radius=7\:cm.}}$

Now the CSA :

We know that,

$\small{\green{\underline{\boxed{\bf{CSA=2\pi\:rh}}}}}$

where,

• π = 22/7
• r is radius = 7 cm
• h is height = 8 cm

Putting the values,

$\small\implies{\sf{CSA=2\times\dfrac{22}{7}\times7\times8}}$

$\small\implies{\sf{CSA=2\times\dfrac{22}{\cancel{7}}\times\cancel{7}\times8}}$

$\small\implies{\sf{CSA=2\times22\times8}}$

$\small\therefore\boxed{\bf{CSA=352\:cm^2.}}$

Now the TSA :

We know that,

$\small{\green{\underline{\boxed{\bf{TSA=2\pi\:r(h+r)}}}}}$

where,

• π = 22/7
• r is radius = 7 cm
• h is height = 8 cm

Putting the values,

$\small\implies{\sf{TSA=2\times\dfrac{22}{7}\times7(8+7)}}$

$\small\implies{\sf{TSA=2\times\dfrac{22}{7}\times7\times15}}$

$\small\implies{\sf{TSA=2\times\dfrac{22}{\cancel{7}}\times\cancel{7}\times15}}$

$\small\implies{\sf{TSA=2\times22\times15}}$

$\small\therefore\boxed{\bf{TSA=660\:cm^2.}}$

Curved surface area = 352 cm².

Total surface area = 660 cm².