Question

Three cubes of aluminum metal of edge 18 cm, 19 cm, and 21 cm respectively are melted and formed a cone of radius 49/11 cm. Find the height of the cone.

1. 21.12 m
2. 10.56 m
3. 12.12 m
4. 23.12 m

Answer 1

Correct Answer - Option 2 : 10.56 m

Given:

Cube of edge 18 cm, 19 cm, and 21 cm.

The radius of cone = 49/11 cm

Formula used:

The volume of cube = side³

The volume of cone = (1/3)πr²h

Calculation:

The volume of newly shaped cube = sum of the volume of all cube

Let the side of three cubes be a₁, a₂, a₃.

The volume of all cube

⇒ (a₁)³ + (a₂)³ + (a₃)³

⇒ (18)³ + (19)³ + (21)³

⇒ 21952

The volume of cone = The volume of all cube

⇒ (1/3)πr²h = 21952

⇒ h = (21952 × 3 × 7 × 11 × 11)/(22 × 49 × 49)

⇒ h = 1056 cm

⇒ h = 10.56 m

∴ The height of the cone is 10.56 m.