Question

A solid cone of base radius 5 cm height 14 cm is melted and recast in to a wire of radius 1 mm. what is the length of the wire?
1. 150 m
2. 35 m
3. 275 m
4. 350/3 m

Answer 1

Correct Answer - Option 4 : 350/3 m

Given:

The radius(r) of the solid cone = 5 cm

The height(h) of the solid cone = 14 cm

The radius(R) of the wire = 1 mm

Formula used:

Volume of the solid cylinder = πr2 h

Where, r = Radius of the solid cylinder, h = height of the solid cylinder

The volume of the cone = 1/3 × πR2H

Where R and H are the radii and the height of the cone respectively.

1 milimetre(mm) = 1/10 centimeter (cm)

1 cm = 100 meter

Calculation:

Let the length of the wire be H cm

According to the question:

The radius of wire in cm = 1/10 cm

Volume of the solid cylinder = Volume of the cone

⇒ πr2 h = 1/3 × πR2H

⇒ (1/10)² × H = (5)² × 14/3

⇒ H = 25 × 14 × 100/3

⇒ H = 35000/3 cm

Length in meter = (35000/3 × 100) = 350/3 m

∴ The length of the wire is 350/3 m.