Three cubes of aluminum metal of edge 18 cm, 19 cm, and 21 cm respecti

1.	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 m2. 10.56 m3. 12.12 m4. 23.12 m
Answer» 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.

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 m2. 10.56 m3. 12.12 m4. 23.12 m

Answer» 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.

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