Question

an open (without the top lid) cylinder with base radius 10.5cm and height 16cm.find it's total surface area​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\:\:\:\:\:\: Given:-\:\:\:\:\:\:\:\:}}$

$\sf\:\:\:\: \bullet radius\:of\: cylinder=10.5cm\\ \\ \sf\:\:\:\: \bullet Height\:of\: cylinder=16cm$

• We have to find the T.S.A of cylinder open from top

$\boxed{\sf{T.S A\:of\: cylinder=2\pi r(h+r)}}$

$\bf\underline{\red{\:\:\:\:\:\:\:\: A.T.Q:-\:\:\:\:\:\:\:\:}}$

• This is open from top So

$\underline{\star{\sf{T.S.A\:open\:at\:top= 2\pi r(h+r)- \pi r{}^{2}}}}$

• Now first the Value of $\sf \pi r{}^{2}$

$\sf:\implies Area\:of\:Top=\dfrac{22}{\cancel7}\times \cancel{10.5}\times 10.5\\ \\ \sf:\implies Area\:of\:top= 22\times 1.5\times 10.5\\ \\ \sf:\implies Area\:of\:Top=346.5cm{}^{2}$

• Now the T.S.A

$\sf:\implies T.S.A=2\times \dfrac{22}{\cancel7}\times \cancel{10.5}(10.5+16)\\ \\ \sf:\implies T.S.A=22\times 1.5\times 26.5\\ \\ \sf:\implies T.S.A=874.5cm{}^{2}$

• So the given cylinder is open from top So it's T.S.A will be

$\sf:\implies T.S.A\:of\: cylinder-Area\:of\:Top\\ \\ \sf\implies T.S.A= 2\pi r(h+r)-\pi r{}^{2}\\ \\ \sf:\implies T.S.A= 874.5-346.5\\ \\ \sf:\implies T.S.A= 528cm{}^{2}$

$\boxed{\sf{T.S.A\:of\:Given\: cylinder= 528cm{}^{2}}}$

Answer 2

$\large{\underline{\underline{\mathbf\green{GIVEN\::}}}}$

• radius of cylinder = 10.5cm

• height of cylinder = 16cm

$\large{\underline{\underline{\mathbf\red{SOLUTION\::}}}}$

$\implies$ the cylinder is open from top ---(I)

$\implies$ T.SA of cylinder = 2πr(h+r)

$\implies$ given, this is open from top,

$\purple{\boxed{.°. \:T.SA \:of\: cylinder \:= 2πr(h+r) \:= \: πr^2}}$

NOW,

$\implies$ T.SA = 2πr(h+r)

$\implies$ 2 × 22/7 ×10.5 (16+10.5)

$\implies$ 22 × 1.5 × 26.5

$\implies$ $\red{\boxed{T.SA =874.5cm^2}}$

Now,

$\implies$ Area of top = πr²

$\implies$ 22/7 × 10.5 ×10.5

$\implies$ 22 × 1.5 ×10.5

$\implies$ $\green{\boxed{.°. Area\: of \:top =346.5cm^2}}$

• According to the (I) statement

$\implies$ T.SA of cylinder - Area of top

$\implies$T.SA of cylinder= 2πr(h+r) - πr²

$\implies$ T.SA of cylinder=(874.5 - 346.5)cm²

$\implies$ $\orange{\boxed{T.SA\: of \:cylinder= \:528cm^2}}$

__________________________

✦SOME RELATED FORMULAE TO THE CYLINDER.

1. CSA of cylinder = 2πrh

2. volume of cylinder = πr²h

3. TSA of cylinder = 2πr(h+r)