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By similar triangles:

$\dfrac{r}{24}=\dfrac{14}{48}$

$r=\dfrac{24(14)}{48}=7$

The lateral area of a frustum of a right circular cone is given by

$S=\dfrac{1}{2}(c_1+c_2)L$

where: $c_1$ = circumference of the upper base, $c_2$ = circumference of the lower base and $L$ = slant height

Substituting, we get

$S=\dfrac{1}{2}\pi(14+28)\sqrt{24^2+7^2}=21\pi(25)=525\pi$

Finally,

$A=$ $\color{#D61F06}\boxed{525}$

The formula for the cone's lateral surface area = $\pi rl$ , where $r$ is the radius of the cone and $l$ is the slant length of the cone.

Now since the cone is cut at half of its height, the radius of the bigger base is twice longer than the smaller one, according to the similar triangles' property, as portrayed in a 2-D presentation of the cone:

As a result, the smaller radius is $7$ cm. long with the height of 24 cm. (half of its original height), and by Pythagorean theorem, the slant height is $\sqrt{7^2 + 24^2} = 25$ cm. for the smaller cone and $50$ cm. for the bigger cone.

Then the lateral surface area of the megaphone is the difference between the lateral surfaces of the bigger and the smaller cone = $(\pi\times 14\times 50) - (\pi\times 7\times 25)$ = $\boxed{525\pi}$ .