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Shot put throw is one of the events in the World Athletics Championships. The shot put ball is spherical in shape with a volume of 4,913,000 cubic millimeters. If it is melted and converted into a cube, what will be the length of the cube?

Answer :

Answer:

The length of the cube is 170 mm

Step-by-step explanation:

Volume of Solids

The volume of a cube of length a is:

[tex]V_c=a^3[/tex]

The shot put ball is spherical with a volume of 4,913,000 cubic millimeters. The ball is melted and converted into a cube, thus we have the volume of the cube.

Let's solve the equation of the volume of the cube for a:

[tex]a=\sqrt[3]{V_c}[/tex]

[tex]a=\sqrt[3]{4,913,000}=170\ mm[/tex]

The length of the cube is 170 mm

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Rewritten by : Barada

To convert the given sphere's volume into a cube, we first find the sphere's radius and then determine the side length of the resulting cube to be approximately 170.98 millimeters.

To solve the problem of converting the sphere's volume into a cube, follow these steps:

  1. Find the radius of the sphere: Use the formula for the volume of a sphere, V = (4/3)πr³, and solve for the radius (r).
  2. Calculate the volume: Given that V = 4,913,000 cubic millimeters, rearrange to solve for r:
    (4/3)πr³ = 4,913,000
    r³ = 4,913,000 × (3/4) / π
    r³ ≈ 1,174,803.45
    r ≈ 103.2 mm.
  3. Convert sphere to cube: The volume of the sphere = volume of the cube, so: s³ = 4,913,000.
    s = ∛4,913,000 ≈ 170.98 mm.

Therefore, the side length of the cube will be approximately 170.98 millimeters.