Question

Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height (π = 3.14).

Answer 1

Let the radius of the base and perpendicular height of the cone be r cm and h cm, respectively.

Slant height of the cone, l = 10 cm

Surface area of the cone = 188.4 cm²

∴ πrl = 188.4 cm² 

⇒ 3.14 × r x 10 = 188.4

⇒ r = `[188.4]/[3.14 xx 10]` = 6 cm

Now,

r² +  h² = l²
⇒ (6)² + h² = (10)²

⇒ 36 + h² = 100

⇒ h² = 100 − 36 = 64

⇒  h = `sqrt 64` = 8 cm.

Thus, the perpendicular height of the cone is 8 cm.