Question

the radius of cone is 3 cm and vertical height is 4 cm. find area of curved surface area​

Answer 1

Answer:47.14

Step-by-step explanation:

L=5 r=3,pie=22/7

Csa=22/7×3×5

66×5/7=330/7=47.14

Answer 2

$\frak{Given} \begin{cases} & \sf{Radius, r = \bf{3\;cm}} \\ & \sf{Height, h = \bf{4\;cm}} \end{cases}$

☯ Let l cm be the slant height of the cone. Then,

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$\setlength{\unitlength}{1cm}\begin{picture}(6, 4)\linethickness{0.26mm} \qbezier(5.8,2.0)(5.8,2.3728)(4.9799,2.6364)\qbezier(4.9799,2.6364)(4.1598,2.9)(3.0,2.9)\qbezier(3.0,2.9)(1.8402,2.9)(1.0201,2.6364)\qbezier(1.0201,2.6364)(0.2,2.3728)(0.2,2.0)\qbezier(0.2,2.0)(0.2,1.6272)(1.0201,1.3636)\qbezier(1.0201,1.3636)(1.8402,1.1)(3.0,1.1)\qbezier(3.0,1.1)(4.1598,1.1)(4.9799,1.3636)\qbezier(4.9799,1.3636)(5.8,1.6272)(5.8,2.0)\put(0.2,2){\line(1,0){2.8}}\put(3.2,4){\sf{4 cm}}\put(5,4){\sf{l cm}}\put(3,2){\line(0,2){4.5}}\put(1.4,1.6){\sf{3 cm}}\qbezier(.185,2.05)(.7,3)(3,6.5)\qbezier(5.8,2.05)(5.3,3)(3,6.5)\put(3,2.02){\circle*{0.15}}\put(2.7,2){\dashbox{0.01}(.3,.3)}\end{picture}$

⠀⠀

$\qquad\star\;\sf l^2 = r^2 + h^2$

$:\implies\sf l^2 = 3^2 + 4^2$

$:\implies\sf l^2 = 9 + 16$

$\qquad:\implies\sf l^2 = 25$

$:\implies\sf \sqrt{l^2} = \sqrt{25}$

$\: :\implies{\boxed{\frak{\pink{l = 5\;cm}}}}\;\bigstar$

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☯ Now, Finding Curved Surface Area of cone,

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We know that,

$\star\;{\boxed{\sf{\purple{CSA_{\;(cone)} = \pi rl}}}}$

$:\implies\sf \dfrac{22}{7} \times 3 \times 5$

$:\implies{\boxed{\frak{\pink{47.14\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Curved\; Surface\;area\;of\;cone\;is\; \bf{47.14\;cm^2}.}}}$

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$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:CSA = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA\\{\quad\:\:\:\qquad=\pi r^2+\pi rl}\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\end{minipage}}$