A semicircular sheet of paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice-cream cup. The depth of the ice-cream cup is :

Answer: Option C

Slant height of the cup, l = Radius of sheet = 14 cm
Circumference of the base :
= Circumference of the paper sheet
= $$\left(\frac{22}{7}\times 14\right)$$  cm
= 44 cm
Let the radius of the base of the cone be r cm
$$\begin{array}{rl}& \therefore 2\pi r=44\\ & \Rightarrow r=\frac{44\times 7}{2\times 22}\\ & \Rightarrow r=7\\ & \text{Height, h:}\\ & =\sqrt{l^2-r^2}\\ & =\sqrt{{\left(14\right)}^2-{\left(7\right)}^2}\\ & =\sqrt{147}\text{ cm}\\ & =7\sqrt{3}\text{ cm}\\ & =12.12\text{ cm}\end{array}$$