▪︎Side 15 cm, 18 cm and x cm form a right angle triangle.
We know that :
[tex] =\tt {hypotenuse}^{2} = {leg}^{2} + {leg}^{2} [/tex]
Which means :
[tex] =\tt {15}^{2} + {x}^{2} = {18}^{2} [/tex]
[tex] =\tt 225 + {x}^{2} = 324[/tex]
[tex] =\tt {x}^{2} = 324 - 225[/tex]
[tex] = \tt {x}^{2} = 99[/tex]
[tex]\color{plum} =\tt x = 9.9 \: cm[/tex]
Thus, x (radius) = 9.9 cm
We know that :
[tex]\color{hotpink}\tt \: Surface \: area \: of \: cone \color{plum}=\pi r(r + \sqrt{ {h}^{2} + {r}^{2} } [/tex]
Then, the surface area of this cone :
[tex] = \tt3.14 \times 9.9 \times( 9.9 + \sqrt{ {15}^{2} + {9.9}^{2} } )[/tex]
[tex] =\tt 3.14 \times 9.9 \times( 9.9 + \sqrt{323.01} )[/tex]
[tex] =\tt 3.14 \times 9.9 \times (9.9 + 18)[/tex]
[tex] =\tt 3.14 \times 9.9 \times 27.9[/tex]
[tex] = \tt31.09 \times 27.9[/tex]
[tex]\color{plum} =\tt\bold{ 867.4 \: cm}[/tex]
Therefore, the surface area of this cone = 867.4 cm
