Final answer:
To find the total volume of the rolling pin, we need to calculate the volume of the spheres and the volume of the cylinder separately and then add them together.
Step-by-step explanation:
The rolling pin is made up of two identical spheres attached to the ends of a cylinder. The diameter of each sphere is 4cm and the diameter of the cylinder is also 4cm. The length of the cylinder is 40cm. To find the total volume of the rolling pin, we need to calculate the volume of the spheres and the volume of the cylinder separately and then add them together.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Since the diameter of each sphere is 4cm, the radius is half of that, which is 2cm. So, the volume of each sphere is (4/3)π(2cm)³. Multiply this by 2 to get the total volume of the spheres.
The volume of the cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The radius of the cylinder is also 2cm and the length of the cylinder is 40cm. So, the volume of the cylinder is π(2cm)²(40cm).
Now, add the volume of the spheres to the volume of the cylinder to get the total volume of the rolling pin.
The total volume of the rolling pin consists of the volume of two spheres and the volume of the central cylinder. To calculate the volume of the cylinder, we use the formula V = πr²h, where r is the radius and h is the height (length) of the cylinder. Given that the diameter is 4 cm, we have a radius of 2 cm for both the spheres and the cylinder. With a cylinder length of 40 cm, the volume of the cylinder is π(2 cm)²(40 cm) = 160π cm³. Each sphere's volume is calculated using the formula volume of a sphere = 4/3 πr³. Therefore, the volume of each sphere is 4/3 π(2 cm)³ = 32/3π cm³. Adding the volume of both spheres and the cylinder, the total volume is 160π + 2(32/3π) cm³, which simplifies to 224/3π cm³.