Question

What is the surface area of the right cone below?

Answer 1

Answer:

213.69 units

Step-by-step explanation:

We have to first find the height of the cone.

We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:

$h^2 = a^2 + b^2$

where h = hypotenuse

a and b = the other two sides of the triangle

The radius is 4 units and the slant height is 13 units:

$13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units$

The height of the cone is 12.37 units.

The surface area of a cone is given as:

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

$SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units$

The surface area of the cone is 213.69 units.