Final answer:
To determine how many whole spheres can be made from the melted cylinder, the volume of the cylinder is first calculated and then divided by the volume of one sphere. Using the provided formulas, it can be deduced that 39 whole spheres of radius 2cm can be made from a solid metal cylinder with a radius of 5cm and length of 17cm.
Step-by-step explanation:
To find out how many spheres can be made from the melted cylinder, we need to calculate the volume of both the cylinder and the spheres and then find the ratio between them.
The volume of the cylinder can be calculated using the formula:
V_{cylinder} = πr^2h
For a cylinder with a radius of 5 cm and a height of 17 cm, this becomes:
V_{cylinder} = 3.14159 × (5 cm)^2 × 17 cm
≈ 1335.3 cm^3
The volume of a sphere can be calculated using the formula:
V_{sphere} = \frac{4}{3}πr^3
For a sphere with a radius of 2 cm, this becomes:
V_{sphere} = \frac{4}{3} × 3.14159 × (2 cm)^3
≈ 33.51 cm^3
To determine how many spheres can be made from the cylinder, divide the volume of the cylinder by the volume of one sphere:
ø39.83 ≈ 39 spheres
Thus, you can make 39 whole spheres from the metal cylinder.