A lead cylinder with a diameter of 25 cm and a heighth of of 40 cm is melted. the lead is used to cast lead spheres with a radius of 3 cm each. calculate how many spheres can be casted from the available lead.
pi (25)^2/4 * 40 = n (4/3) pi (3)^3
6250 = 36 n
25-40×160
-6375
To find out how many spheres can be cast from the available lead, we need to calculate the volume of the lead cylinder and the volume of each lead sphere.
The volume of a cylinder is given by the formula: V_cylinder = π * r^2 * h, where r is the radius and h is the height.
Given that the diameter of the cylinder is 25 cm, we can calculate the radius by dividing the diameter by 2:
r = 25 cm / 2 = 12.5 cm.
The height of the cylinder is 40 cm.
Now we can substitute these values into the formula to calculate the volume of the cylinder:
V_cylinder = π * (12.5 cm)^2 * 40 cm.
Next, let's calculate the volume of each lead sphere. The volume of a sphere is given by the formula: V_sphere = (4/3) * π * r^3, where r is the radius.
Given that the radius of each sphere is 3 cm, we can substitute this value into the formula to calculate the volume of each sphere:
V_sphere = (4/3) * π * (3 cm)^3.
Now, to determine how many spheres can be cast from the available lead, we need to divide the volume of the cylinder by the volume of each sphere:
Number of spheres = V_cylinder / V_sphere.
By substituting the calculated values into this equation, we can determine the number of spheres that can be cast from the available lead.