# An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone.

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An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high  and the conical part is 36 cm high. Find the weight of the pillar if one cubic cm of iron weight is 7.8 grams.

answered Mar 27 by (-4,746 points)

Let r1 cm and r2 cm denote the radii of the base of the cylinder and cone respectively. Then,

r1 = r2 = 8 cm

Let h1 and h2 cm be the height of the cylinder and the cone respectively. Then

h1 = 240 cm and h2 = 36 cm Now, volume of the cylinder = πr12h1 cm3

= (π × 8 × 8 × 240)cm3

= (π × 64 × 240) cm3

Volume of the cone = 1/3πr22h2 cm3

= (1/3π × 8 × 8 × 36) cm3

= (1/3π × 64 × 36) cm3

∴   Total volume of iron = Volume of the cylinder + Volume of the cone

= (π × 64 × 240 + 1/3π × 64 × 36) cm3

= π × 64 × (240 + 12) cm3

= 22/7 × 64 × 252 cm3

= 22 × 64 × 36 cm3

Hence, total weight of the pillar = Volume Weight per cm3

= (22 × 64 × 36) × 7.8 gms

= 395366.4 gms

= 395.3664 kg.