# If the Ratio of Radius of Base and Height of a Cone is 5:12 and Its Volume is 314 Cubic Metre. Find Its Perpendicular Height and Slant Height ( π = 3 . 14 ) - Geometry

Sum

If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height (π = 3.14 )

#### Solution

The ratio of radius of base and perpendicular height of a cone is 5 : 12.
Let the radius of base and perpendicular height of the cone be 5x and 12x, respectively.

Volume of the cone = 314 m3

∴ 1/3πr2h = 314 m3

⇒ 1/3 x 3.14 x (5x )2 x 12x = 314

⇒ 314 x3 = 314

⇒ x3 = 1

⇒  x = 1

∴ Perependicular height of the cone = 12x = 12 × 1 = 12 m
Radius of the cone = 5x = 5 × 1 = 5 m

Now,
(Slant height)2 = (Perpendicular height)+ (Radius)2
⇒ (Slant height)2 = (12)+ (5)2
⇒ (Slant height)2 = 144 + 25 = 169
⇒ (Slant height)2 = (13)2
⇒ Slant height = 13 m

Thus, the perpendicular height and slant height of the cone is 12 m and 13 m, respectively.

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#### APPEARS IN

Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 9 Surface Area and Volume
Problem Set 9 | Q 3 | Page 123