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 .