A hollow metallic cylindrical tube has an internal radius of 3 cm and height 21 cm. The thickness of the metal is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.
Mensuration
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Question

A hollow metallic cylindrical tube has an internal radius of 3 cm and height 21 cm. The thickness of the metal is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.

Mensuration

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KnowledgeBoat · Accepted Answer

Internal radius (r) = 3 cm Height (h) = 21 cm Thickness = External radius (R) - Internal radius ⇒ 0.5 = External radius - 3 cm ⇒ External radius = 0.5 + 3 = 3.5 cm Volume of hollow cylinder = π(R2 - r2)h, Putting values we get, ∴ Volume of metal = π(3.52 - 32) × 21 Given the tube is melted and cast into a right circular cone of height (H) 7 cm. So, the volume of metal and volume of cone will be same. ∴ 214.5 = πr2H Hence, radius of the cone is 5.4 cm.

Mathematics

A hollow metallic cylindrical tube has an internal radius of 3 cm and height 21 cm. The thickness of the metal is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.

Mensuration

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