Question

The height of cone is 16 cm and its base radius is 12 cm. Find the curved surface area and the total surface area of the cone. (Use π = 3.14)

Answer 1

Given:

Height h = 16 cm

base radius r = 12 cm.

Slant height: l = `sqrt(h^2 + r^2)`

Curved surface area (CSA) = π r l

Total surface area (TSA) = π r l + π r² = π r (l + r).

Step 1:

Find slant height l: `l = sqrt(h^2 + r^2)`

= `sqrt(16^2 + 12^2)`

= `sqrt(256 + 144)`

= `sqrt(400)`

= 20 cm.

Step 2:

Curved surface area:

CSA = π r l

= 3.14 × 12 × 20

= 3.14 × 240

= 753.6 cm²

Base area: Base

= `π r^2 = 3.14 × 12^2`

= 3.14 × 144

= 452.16 cm²

Total surface area:

TSA = CSA + base

= 753.6 + 452.16

= 1205.76 cm².