Question

find total surface area of cone whose diameter of base is 8 cm and height is 3 cm​

Answer 1

Answer:

SA≈ 113.1

Step-by-step explanation:

R= D/2

R= 8/2

R= 4 cm

SA= $\pi r(r+\sqrt{h^{2}+r^{2})$

SA= $3.14 times 4 (4+\sqrt{3^{2} +4^{2} )$

SA= 113.1

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Answer 2

$\huge\mathbb{\underline{\underline{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{Base\: Diameter=8cm}\\ \sf{Radius=\frac{\cancel8}{\cancel2}=4}\\ \sf{Height =3cm}\end{cases}$

$\bold{To\:Find}$

The total surface area of cone

$\sf Total \:surface\:area\:of\:cone=\pi r (l+r)$

• Slant height =L

Now

.$\sf( slant \:height){}^{2}=(Height){}^{2}+(radius){}^{2}$

$\sf\implies l{}^{2}=h{}^{2}+r{}^{2}\\ \\ \sf\implies l{}^{2}=(3){}^{2}+(4){}^{2}\\ \\ \sf\implies l{}^{2}=9+16\\ \\ \sf\implies L=\sqrt{25}\\ \\ \sf\implies l=5cm$

• The slant height =5cm

• Now find the total surface area of cone

$\sf Total\:surface\:area=\pi r(l+r)\\ \\ \sf\implies by\:taking\: \pi=\frac{22}{7}\\ \\ \sf\leadsto T.S.A=\frac{22}{7}\times 4(5+4)\\ \\ \sf\leadsto T.S.A=\frac{22}{7}\times 4\times 9 \\ \\ \sf\leadsto T.S.A=\frac{22}{7}\times 4\times 9\\ \\ \sf\leadsto T.S.A=\frac{22\times 4\times 9}{7}\\ \\ \sf\leadsto Total \: surface\:area=\frac{\cancel{792}}{\cancel7}=113.14cm{}^{2}$

$\boxed{\underline{\mathbb{T.S.A \:OF\:CONE=113.14cm{}^{2}}}}$

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