The surface area of the cone is 9.42cm²
Explanation:
When a triangle with the interior angle as 30°-60°-90° is rotated then a cone is formed.
So, we need to find the surface area of the cone.
Surface area of a cone is πr
² + πrl
where,
r = radius of the cone
l = lateral height of the cone
tan (30°) = [tex]\frac{perpendicular}{base} =\frac{BC}{AB} =\frac{1}{\sqrt{3} }[/tex]
So,
BC = 1
AB = √3
AC = ?
(AC)² = (BC)² + (AB)²
(AC)² = (1)² + (√3)²
AC = 2
Lateral height, h = 2cm
Radius = BC = 1cm
Thus,
surface area of the cone = πr
² + πrl
[tex]=\pi (1)^2 + \pi X 1 X 2\\\\=\pi + 2\pi \\\\=3\pi \\\\= 9.42 cm^2[/tex]
Therefore, surface area of the cone is 9.42cm²
