Question

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find. 
(i) radius of the base and 
(ii) total surface area of the cone.

Answer 1

(i) Slant height (l) of cone = 14 cm
Let the radius of the circular end of the cone be r.
We know, CSA (Curved surface area) of cone = \(\pi rl\)
\(\pi rl\) = 308

\(r = \frac{308 cm²}{\pi l}\)

\(r =\frac{ 308 cm²}{14 cm} \times \frac{7}{22}\)
= 7 cm
Therefore, the radius of the circular end of the cone is 7 cm.

---

(ii) Total surface area of cone = CSA of cone + Area of base
\(=\pi r (l + r)\)

= \(\frac{22}{7} \)× 7 cm × (7 cm + 14 cm)

= 22 cm × 21 cm
= 462 cm²
Therefore, the total surface area of the cone is 462 cm2 .