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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)
Solution
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 x 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.
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