A1. If we were to unfold the cone's lateral surface onto a plane, we would get a quarter of a circle with a radius of $8 \mathrm{~cm}$. How tall is the cone?
(A) $10 \mathrm{~cm}$
(B) $2 \sqrt{15} \mathrm{~cm}$
(C) $\sqrt{20} \mathrm{~cm}$
(D) $3 \mathrm{~cm}$
(E) $16 \mathrm{~cm}$
A1. Considering that the radius of the circular sector is equal to the slant height of the cone $s=8 \mathrm{~cm}$. The length of the circular arc of the unfolded lateral surface of the cone is equal to the circumference of the base of the cone $\frac{1}{4} \cdot 2 \pi s=2 \pi r$. Calculation of the radius of the cone $r=\frac{s}{4}=2 \mathrm{~cm}$. Calculation of the height of the cone $v^{2}=s^{2}-r^{2}=8^{2}-2^{2}$, $v=\sqrt{60} \mathrm{~cm}=2 \sqrt{15} \mathrm{~cm}$.