asolid metal cube of side 10cm is melted down and recast as solid metal sphere.calculate the radius of the sphere.Take Pie=3.142
r≈5.64
Using the formula
A=2πrh+2πr2
Solving for r
r=1/2 √(h^2+(2A/π))﹣h/22
To calculate the radius of the sphere, we can use the concept of conservation of volume.
The volume of the cube can be calculated by using the formula V = s^3, where V is the volume and s is the side length of the cube. In this case, the side length of the cube is 10 cm, so the volume of the cube is V_cube = 10^3 = 1000 cm^3.
According to the conservation of volume, the volume of the sphere should be equal to the volume of the cube. The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.
Therefore, we can set up the equation V_cube = V_sphere and solve for the radius of the sphere.
Using the given value of π = 3.142 and V_cube = 1000 cm^3, the equation becomes:
1000 = (4/3) * 3.142 * r^3
Now, we can solve this equation for r:
r^3 = (1000 * 3) / (4 * 3.142)
r^3 = 750 / 3.142
r^3 ≈ 238.682
r ≈ ∛238.682
Using a calculator, we find that r ≈ 6.74 cm (rounded to two decimal places).
Therefore, the radius of the sphere is approximately 6.74 cm.
4/3 πr^3 = 10^3
r^3 = 3000 / 4π
r = 6.2