A semi-circular lamina of radius 35 cm is folded so that the two bounding radii are joined together to form a cone. Find :

(i) the radius of the cone.

(ii) the (lateral) surface area of the cone.

(i) Length of the arc of the semi-circular sheet = $\dfrac{1}{2} \times 2πr$

= πr = $\dfrac{22}{7}$ x 35 = 110 cm

Let r cm be the radius of the cone, then

$2πr = 110 \\[1em] 2 \times \dfrac{22}{7} \times r = 110 \\[1em] r = \dfrac{110 \times 7}{2 \times 22} \\[1em] r = \dfrac{770}{44} \\[1em] r = 17.5 \text{ cm}.$

Hence, the radius of the cone is 17.5 cm.

(ii) Curved surface area of cone = area of semi-circular sheet.

$= \dfrac{1}{2} \times πr^2 \\[1em] = \dfrac{1}{2} \times \dfrac{22}{7} \times (35)^2 \\[1em] = \dfrac{22}{14} \times 1225 \\[1em] = \dfrac{26950}{14} \\[1em] = 1925 \text{ cm}^2$

Hence, the curved surface area of the cone = 1925 cm².