Question

A solid metallic right circular cylinder is 1.8 m high with diameter of its base 2 m is melted and recased into right circular cone with base of diameter 3 m.Find the height of the cone.

Answer 1

Answer:

•If solid of one shape is converted into solid of another shape then, Total volume of the solid to be converted= Total volume of the solids into which the given solid is to be converted.

SOLUTION:

GIVEN:

Height of a solid metallic right circular cylinder (h) = 1.8 m

Diameter of a solid metallic right circular cylinder (d) = 2m

Radius of a solid metallic right circular cylinder (r) = d/2 = 2/2 = 1m

Diameter of a circular cone (D) = 3m

Radius of a circular cone (R) = D/2 = 3/2 m

Let ,H be the height of a circular cone.

Volume of Cylinder = Volume of Cone

πr²h = ⅓ (πR²H)

1² × 1.8 = ⅓ (3/2)² × H

1.8 × 3 = 9/4 ×H

1.8 × 3 × 4 = 9H

H = (1.8 × 3 × 4)/9 = 0.6 ×4 = 2.4 m

Hence, the height of the cone is 2.4 m.

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