Question

Find the following
i) Volume
ii) Curved Surface Area
iii) Total Surface Area



A metal pipe which is hollow has radius of 7 cm and height of 14 cm.​

Answer 1

Radius of the Cylinder(r) = 7cm

and height (h) = 15cm

(i) Curved surface area=

2πrh

=2×22

7×7×15

=660cm

(ii) Total surface area =

2πr(h+r)

=2×22

7×7(15+7)cm

=44×22

=968cm

(iii) Volume =

πr2h=22

7×7×7×15cm

=2310cm

please give me brain list and thanks

Answer 2

$\star \; {\underline{\boxed{\pmb{\purple{\sf{ \; Given \; :- }}}}}}$

• Radius of Pipe = 7 cm
• Height of Pipe = 14 cm

$\\ \rule{200pt}{3pt}$

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; To \; Find \; :- }}}}}}$

• Curved Surface Area
• Total Surface Area
• Volume

$\\ \rule{200pt}{3pt}$

$\star \; {\underline{\boxed{\pmb{\color{darkblue}{\sf{ \; SolutioN \; :- }}}}}}$

$\maltese \; {\underline{\textbf{\textsf{ Formula \; Used \; :- }}}}$

$\qquad \; {\bigstar \; {\underline{\overline{\boxed{\pmb{\sf{ \begin{array}{cc} \longmapsto \; {\sf{ Curved \; Surface \; Area = 2 \pi rh }} \\ \\ \longmapsto \; {\sf{ Total \; Surface \; Area = 2 \pi r \bigg( r + h \bigg) }} \\ \\ \longmapsto \; {\sf{ Volume = \pi {r}^{2} h }} \end{array} }}}}}}} \; \bigstar$

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\textbf{\textsf{ Curved \; Surface \; Area \; :- }}}}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { CSA = 2 \pi rh } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { CSA = 2 \times \dfrac{22}{7} \times 7 \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { CSA = 2 \times \dfrac{22}{\cancel7} \times \cancel7 \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { CSA = 2 \times 22 \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { CSA = 44 \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; {\underline{\boxed{\pmb{\sf{ CSA = 616 \; {cm}^{2} }}}}} \; {\pink{\bigstar}} \\ \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\textbf{\textsf{ Total \; Surface \; Area \; :- }}}}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \sf { TSA = 2 \pi r \bigg( r + h \bigg) } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \sf { TSA = 2 \times \dfrac{22}{7} \times 7 \times \bigg( 7 + 14 \bigg) } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \sf { TSA = 2 \times \dfrac{22}{7} \times 7 \times 21 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \sf { TSA = 2 \times \dfrac{22}{\cancel7} \times \cancel7 \times 21 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \sf { TSA = 2 \times 22 \times 21 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \sf { TSA = 44 \times 21 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; {\underline{\boxed{\pmb{\sf{ TSA = 924 \; {cm}^{2} }}}}} \; {\orange{\bigstar}} \\ \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\textbf{\textsf{ Volume \; :- }}}}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { Volume = \pi {r}^{2} h } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { Volume = \dfrac{22}{7} \times {(7)}^{2} \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { Volume = \dfrac{22}{7} \times 49 \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { Volume = \dfrac{22}{\cancel7} \times \cancel{49} \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { Volume = 22 \times 7 \times 14 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; \sf { Volume = 22 \times 98 } \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; :\implies \; {\underline{\boxed{\pmb{\sf{ Volume = 2156 \; {cm}^{3} }}}}} \; {\purple{\bigstar}} \\ \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\therefore \;$ Curved Surface Area of Pipe is 616 cm² and Total Surface and Volume are 924 cm² and 2156 cm³ respectively .

$\\ {\underline{\rule{300pt}{9pt}}}$