Question

1. Find the lateral area of a cone with a radius of 7 ft. and a slant height of 13 ft. Use 3.14 for pi and round to the nearest tenth.

(I don't need a website for this. I just need someone to please explain how to do this. I have no idea on how this works. Can someone just please explain step-by-step on how to solve this?)

Answer 1

if you cut the cone along the slant height, and flatten it
... you will see that it forms a partial disc

the slant height becomes the radius of the disc

the fraction of the disc is ... (cone base circumference) / (disc circumference)

the L.A. of the cone is the area of the fraction of the disc

Answer 2

Even though there are formulas for this, let's analyse it.
Sketch a cone, sketch the right-angled triangle with a base of 7, a height of h
and a hypotenuse of 13
h^2 + 7^2 = 13^2
h = √120

Now visualize cutting the cone along the edge and laying it out flat.
(think of cutting open a cone-shaped drinking cup from a water dispenser)

We want the surface area of that sector!!

You will have a sector of a circle with radius 13 and an arc-length equal to
the circumference of the base of the cone.
circumference of base of cone = 2π(7) = 14π
circumference of the circle that forms our sector = 2π(13) = 26π

Area of the whole circle that forms our sector = π(13)^2 = 169π

using ratios:
area of sector/169π = 14π/26π = 7/13
area of sector = (7/13)(169π) = .....