Final answer:
The number of solid spheres that can be moulded into a cylinder, we first find the volumes of one sphere and the cylinder and then divide the volume of the cylinder by the volume of the sphere. It turns out that 5 spheres, each with a diameter of 6 cm, can be moulded to form a cylinder with a height of 45 cm and a diameter of 4 cm.
Step-by-step explanation:
To find the number of solid spheres that could be moulded to form a solid metallic cylinder, we need to calculate the volume of both shapes and then divide the volume of the cylinder by the volume of a single sphere.
The volume of a sphere can be calculated using the formula V = 4/3 π r³, where r is the radius of the sphere. Since the diameter of the sphere is 6 cm, the radius is 3 cm. Therefore, the volume V of one sphere is:
V = 4/3 π (3 cm)³ = 36π cm³
The volume of the cylinder is calculated using the formula V = π r³ h, where R is the radius and h is the height of the cylinder. For a cylinder with a diameter of 4 cm and height of 45 cm, the radius R is 2 cm and we get:
V = π (2 cm)³ (45 cm) = 180π cm³
Now, to find the number of spheres that can be moulded into the cylinder, divide the cylinder's volume by the sphere's volume:
Number of spheres = 180π cm³ / 36π cm³ = 5
Therefore, 5 spheres can be moulded to form the given cylinder.