Question

${\LARGE {\mathfrak{\underline {QUESTION}}}}$

$\sf Find \:the\:TSA\:of\:cylinder \:of \:radius \:7\:m\\\sf and\:height\:14\:m$

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt Find\: the\: TSA\: of \:cylinder \:of\: radius\: 7 \:m\: and\\\tt height\: 14\:m$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

$\bf Radius \:of\: the\: cylinder = 7\:m$

$\bf Height\: of\: the \:cylinder = 14\:m$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

$\bf Total surface area of the cylinder$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Total\: surface\: area\: of \:the \:cylinder}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {TSA_{(Cylinder)}=2\pi r\big(r+h\big)}}}}}}}$

• $\sf TSA =total \:surface \:area \:of \:the \:cylinder$
• $\sf r =radius \:of \:the \:cylinder$
• $\sf h= height \:of \:the \:cylinder$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies TSA=2\times \dfrac{22}{7}\times 7\big(7+14\big)$

$\bf \implies TSA=2\times \dfrac{22}{\cancel{7}}\times \cancel{7}\big(21\big)$

$\bf \implies TSA=44\times 21$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {TSA=924\:{m}^{2}}}}}}}$

${\underbrace {\red {\underline {\red {\overline {\red {\pmb {\sf {{\therefore} The\:TSA\:of\:the \:cylinder \:is\:924\:{m}^{2}}}}}}}}}}$

_________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf CSA\:of \:the \:cylinder =2\pi r h$

$\sf TSA\:of \:the \:cylinder =2\pi r(r+h)$

$\sf Volume\:of \:the \:cylinder =\pi{r}^{2}h$

Answer 2

Answer:

924 m²

Step-by-step explanation:

Given -

Radius of cylinder (r) = 7 m

Height of cylinder (h) = 14 m

To find -

T. S. A. (Total Surface Area) of cylinder

Solution -

T. S. A. of cylinder = 2πr (h + r)

$= 2 \times \frac{22}{7} \times 7 \times (14 + 7) {m}^{2} \\ = 44 \times 21 {m}^{2} \\ = 924 {m}^{2}$

Hence T. S. A. of cylinder =924 m²

Mote to know :-

T. S. A of cylinder = 2πr (h+r)

C. S. A of cylinder = 2πrh

Volume of cylinder = πr²h

We can also prove these formulas by opening the cylinder into rectangle. And in the rectangle the breadth will be circumference of base and length will be height.

hope it helps.