Answer :
[tex] \pi rl/2 + \pi r^{2}/2 +d( l^{2} - d^{2}/4)/2 [/tex]
if its divided through the top vertex A.
d is the diametre.
then ur cone will have 3 planes....curved,triangular(side),semi circular(bottom).
answer= 23.56+14.13+48=85.69.
if its divided through the top vertex A.
d is the diametre.
then ur cone will have 3 planes....curved,triangular(side),semi circular(bottom).
answer= 23.56+14.13+48=85.69.
[tex]\bf Given \begin{cases} & \sf{Radius,\; r = \bf{3\;cm}} \\ & \sf{Height, \;h = \bf{5\;cm}} \end{cases}\\ \\[/tex]
To find: Total surface area of a piece?
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
[tex]\underline{\sf{\bigstar\; According\;to\;the\;Question\;:}}\\ \\[/tex]
A solid cone is cut by a plane through the vertex A into two equal pieces.
⠀⠀
[tex]\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(4.9,4){\sf{5 cm}}\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)}\multiput(3,1.2)(0,0.5){11}{\line(0,1){0.2}}\end{picture}[/tex]
⠀⠀
Now,
⠀⠀
We know that,
⠀⠀
[tex]\star\;{\boxed{\sf{\purple{TSA_{\;(cone)} = \pi r(r + l)}}}}\\ \\[/tex]
Putting values,
⠀⠀
[tex]:\implies\sf \dfrac{22}{7} \times 3 \bigg(3 + 5 \bigg)\\ \\[/tex]
[tex]:\implies\sf \dfrac{66}{7} \bigg(3 + 5 \bigg)\\ \\[/tex]
[tex]:\implies\sf \dfrac{66}{7} \times 8\\ \\[/tex]
[tex]:\implies{\boxed{\frak{\pink{75.42\;cm^2}}}}\;\bigstar\\ \\[/tex]
[tex]\therefore\;{\underline{\sf{The\;total\;surface\;area\;of\;cone\;is\; \bf{75.42\;cm^2}.}}}[/tex]
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
It is divided into two pieces.
⠀⠀
Therefore,
⠀⠀
Total surface area of a single piece is,
⠀⠀
[tex]:\implies\sf \dfrac{75.42}{2}\\ \\[/tex]
[tex]:\implies{\boxed{\frak{\pink{37.71\;cm^2}}}}\;\bigstar\\ \\[/tex]
[tex]\therefore\;{\underline{\sf{Hence,\;The\;total\;surface\;area\;of\;a\;piece\;cone\;is\; \bf{37.71\;cm^2}.}}}[/tex]