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
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:
- 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).
- 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. - 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.