Your friend’s cap is in the shape of a right circular cone of base radius 14 cm and height 26.5 cm. The approximate area of the sheet required to make 7 such caps is

A cone is formed when the 2 edges of the sector of a circle are joined. 

We have to find the central angle subtended to find out the area of the sheet required to make the cone. 
It has been given that the height of the cone is 26.5 cm and the base radius is 14 cm. 

The slant height of the cone will be equal to the radius of the sector of the circle. 

Slant height = $$\sqrt{26.5^2+14^2}$$ = $$\sqrt{898.25}$$
$$\sqrt{898.25}$$ is very close in value to $$\sqrt{900}$$

Let us use $$\sqrt{900}$$ for the ease of calculation.
$$\sqrt{900}$$ = $$30$$ cm.
Area of sheet required to make 1 cap = Curve surface area of the cone = $$(\pi)rl$$ = (22/7)*14*30 =1320

Area of sheet required to make 7 cap = 7*1320 = 9240 sq cm