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प्रश्न
Curved surface area of a cone is 251.2 cm2 and radius of its base is 8 cm. Find its slant height and perpendicular height. (π = 3.14)
उत्तर
Let the perpendicular height and slant height of the cone be h cm and l cm, respectively.
Radius of the base of cone, r = 8 cm
Curved surface area of the cone = 251.2 cm2
∴ πrl = 251.2 cm2
⇒ 3.14 x 8 x l = 251.2
⇒ l = `251.2/25.12` = 10 cm
Now,
r2 + h2 = l2
⇒ (8)2 + h2 = (10)2
⇒ 64 + h2 = 100
⇒ h2 = 100 - 64 = 36
⇒ h = `sqrt36` = 6 cm
Thus, the slant height and perpendicular height of the cone are 10 cm and 6 cm, respectively.
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