if the circumference of the base of cylinder is 44cm and the sum of its radius and height is 27 cm, find its total surface area. About the author Bella
Answer: [tex]\sf Given \begin{cases} & \sf{Circumference\:of\:the\:base\;of\:cylinder = \bf{44\:cm}} \\ & \sf{Sum\:of\:radius\:and\:height\:of\:cylinder = \bf{27\:cm}} \end{cases}\\ \\[/tex] To find: Total surface area of cylinder? ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀ ☯ Let’s consider r and h be the radius and height of cylinder respectively. ⠀⠀⠀⠀ [tex]\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\[/tex] [tex]\star\;{\boxed{\sf{\pink{Circumference_{\;(circle)} = 2 \pi r}}}}\\ \\[/tex] [tex]:\implies\sf 2 \times \dfrac{22}{7} \times r = 44 \\ \\[/tex] [tex]:\implies\sf \dfrac{44}{7} \times r = 44\\ \\[/tex] [tex]:\implies\sf r = \cancel{44} \times \dfrac{7}{ \cancel{44}}\\ \\[/tex] [tex]:\implies{\underline{\boxed{\frak{\purple{r = 7\:cm}}}}}\;\bigstar\\ \\[/tex] [tex]\therefore\:{\underline{\sf{Radius\:of\:cylinder\:is\: {\textsf{\textbf{7\:cm}}}.}}}[/tex] ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀ [tex]\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\[/tex] Sum of radius and height of cylinder is 27 cm. ⠀⠀⠀⠀ [tex]:\implies\sf r + h = 27\\ \\[/tex] [tex]:\implies\sf 7 + h = 27\\ \\[/tex] [tex]:\implies\sf h = 27 – 7\\ \\[/tex] [tex]:\implies{\underline{\boxed{\frak{\purple{h = 20\:cm}}}}}\;\bigstar\\ \\[/tex] [tex]\therefore\:{\underline{\sf{Height\:of\:cylinder\:is\: {\textsf{\textbf{20\:cm}}}.}}}[/tex] ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀ ☯ Now, Finding Curved surface area of cylinder, ⠀⠀⠀ [tex]\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}\\ \\[/tex] [tex]:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \bigg( 7 + 20 \bigg)\\ \\[/tex] [tex]:\implies\sf 2 \times 22 \times 27\\ \\[/tex] [tex]:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar\\ \\[/tex] [tex]\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}[/tex] Reply
Answer: [tex]\huge{\tt{\red{}\green{A}\purple{N}\pink{S}\blue{W}\orange{E}\red{R}}}[/tex] [tex] ⠀⠀⠀ \begin{gathered}\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}\\ \\\end{gathered}[/tex] [tex]⋆Totalsurfacearea(rectangle)=2πr(r+h) [/tex] [tex]⟹2×722×7(7+20) [tex]⟹2×722×7(7+20)[/tex] [tex]⟹2×22×27 [tex]⟹2×22×27[/tex] [tex]\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar\\ \\\end{gathered}[/tex] [tex]:⟹1188cm2★ [tex]:⟹1188cm2★[/tex] [tex]\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}∴Totalsurfaceareaofcylinderis1188cm2. [tex]\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}∴Totalsurfaceareaofcylinderis1188cm2.[/tex] Reply
Answer:
[tex]\sf Given \begin{cases} & \sf{Circumference\:of\:the\:base\;of\:cylinder = \bf{44\:cm}} \\ & \sf{Sum\:of\:radius\:and\:height\:of\:cylinder = \bf{27\:cm}} \end{cases}\\ \\[/tex]
To find: Total surface area of cylinder?
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☯ Let’s consider r and h be the radius and height of cylinder respectively.
⠀⠀⠀⠀
[tex]\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\[/tex]
[tex]\star\;{\boxed{\sf{\pink{Circumference_{\;(circle)} = 2 \pi r}}}}\\ \\[/tex]
[tex]:\implies\sf 2 \times \dfrac{22}{7} \times r = 44 \\ \\[/tex]
[tex]:\implies\sf \dfrac{44}{7} \times r = 44\\ \\[/tex]
[tex]:\implies\sf r = \cancel{44} \times \dfrac{7}{ \cancel{44}}\\ \\[/tex]
[tex]:\implies{\underline{\boxed{\frak{\purple{r = 7\:cm}}}}}\;\bigstar\\ \\[/tex]
[tex]\therefore\:{\underline{\sf{Radius\:of\:cylinder\:is\: {\textsf{\textbf{7\:cm}}}.}}}[/tex]
⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀
[tex]\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\[/tex]
Sum of radius and height of cylinder is 27 cm.
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[tex]:\implies\sf r + h = 27\\ \\[/tex]
[tex]:\implies\sf 7 + h = 27\\ \\[/tex]
[tex]:\implies\sf h = 27 – 7\\ \\[/tex]
[tex]:\implies{\underline{\boxed{\frak{\purple{h = 20\:cm}}}}}\;\bigstar\\ \\[/tex]
[tex]\therefore\:{\underline{\sf{Height\:of\:cylinder\:is\: {\textsf{\textbf{20\:cm}}}.}}}[/tex]
⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀
☯ Now, Finding Curved surface area of cylinder,
⠀⠀⠀
[tex]\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}\\ \\[/tex]
[tex]:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \bigg( 7 + 20 \bigg)\\ \\[/tex]
[tex]:\implies\sf 2 \times 22 \times 27\\ \\[/tex]
[tex]:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar\\ \\[/tex]
[tex]\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}[/tex]
Answer:
[tex]\huge{\tt{\red{}\green{A}\purple{N}\pink{S}\blue{W}\orange{E}\red{R}}}[/tex]
[tex]
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\begin{gathered}\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}\\ \\\end{gathered}[/tex]
[tex]⋆Totalsurfacearea(rectangle)=2πr(r+h)
[/tex]
[tex]⟹2×722×7(7+20)
[tex]⟹2×722×7(7+20)[/tex]
[tex]⟹2×22×27
[tex]⟹2×22×27[/tex]
[tex]\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar\\ \\\end{gathered}[/tex]
[tex]:⟹1188cm2★
[tex]:⟹1188cm2★[/tex]
[tex]\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}∴Totalsurfaceareaofcylinderis1188cm2.
[tex]\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}∴Totalsurfaceareaofcylinderis1188cm2.[/tex]