A cone has a slant height of 9 cm and a base radius of 7 cm. Find (i) its curved surface area (ii) total surface area.

We have

Given: radius of the base of the cone, r = 7 cm

Slant height of the cone, l = 9 cm

(i). Curved surface area of cone is given by

CSA = πrl

⇒ CSA = 22/7 × 7 × 9

⇒ CSA = (22 × 7 × 9)/7

⇒ CSA = 198

Thus, curved surface area of cone is 198 cm².

(ii). For total surface area of cone, just add surface area of base of cone to the curved surface area of cone.

So, we have

Total surface area = curved surface area + area of base of the cone (area of solid circle)

⇒ TSA = πrl + πr²

⇒ TSA = πr (l + r)

⇒

⇒ TSA = 22 × (9 + 7)

⇒ TSA = 22 × 16

⇒ TSA = 352

Thus, total surface area of cone is 352 cm².