Question

Hey, can you guys help me out with this question? I need the workings too.( find the surface area )

Answer 1

▪︎Side 15 cm, 18 cm and x cm form a right angle triangle.

We know that :

$=\tt {hypotenuse}^{2} = {leg}^{2} + {leg}^{2}$

Which means :

$=\tt {15}^{2} + {x}^{2} = {18}^{2}$

$=\tt 225 + {x}^{2} = 324$

$=\tt {x}^{2} = 324 - 225$

$= \tt {x}^{2} = 99$

$\color{plum} =\tt x = 9.9 \: cm$

Thus, x (radius) = 9.9 cm

We know that :

$\color{hotpink}\tt \: Surface \: area \: of \: cone \color{plum}=\pi r(r + \sqrt{ {h}^{2} + {r}^{2} }$

Then, the surface area of this cone :

$= \tt3.14 \times 9.9 \times( 9.9 + \sqrt{ {15}^{2} + {9.9}^{2} } )$

$=\tt 3.14 \times 9.9 \times( 9.9 + \sqrt{323.01} )$

$=\tt 3.14 \times 9.9 \times (9.9 + 18)$

$=\tt 3.14 \times 9.9 \times 27.9$

$= \tt31.09 \times 27.9$

$\color{plum} =\tt\bold{ 867.4 \: cm}$

Therefore, the surface area of this cone = 867.4 cm