Cylindrical groove is made in a cylindrical piece of wood of length 17.5cm. The groove is filled with graphite and the cylindrical graphite block is of same length as that of wooden piece. If the diameter of the graphite cylinder is 3mm and outer diameter of the wooden cylinder is 10mm. find the volume of the wood and volume of the graphite used
To find the volume of the wood cylinder, we need to calculate the volume of the outer cylinder and subtract the volume of the inner cylinder.
1. Volume of the outer wooden cylinder:
The diameter of the wooden cylinder is given as 10mm, which means the radius is half of that, i.e., 5mm or 0.5cm.
The length of the wooden cylinder is given as 17.5 cm.
Using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height, we can calculate the volume as follows:
V_wood = π(0.5)^2 × 17.5
2. Volume of the inner graphite cylinder:
The diameter of the graphite cylinder is given as 3mm, which means the radius is half of that, i.e., 1.5mm or 0.15cm.
The length of the graphite cylinder is the same as that of the wooden cylinder, i.e., 17.5 cm.
Again, using the formula for the volume of a cylinder, we calculate the volume as follows:
V_graphite = π(0.15)^2 × 17.5
Therefore, the volume of the wood cylinder is V_wood and the volume of the graphite cylinder is V_graphite.
To find the volume of the wood and the volume of the graphite used, we first need to calculate the dimensions of each cylinder.
1. Calculate the radius of the graphite cylinder:
The diameter of the graphite cylinder is given as 3mm. The radius is half of the diameter, so the radius is 3mm / 2 = 1.5mm.
2. Calculate the radius of the wooden cylinder:
The outer diameter of the wooden cylinder is given as 10mm. The radius is half of the diameter, so the radius is 10mm / 2 = 5mm.
3. Calculate the lengths of both cylinders:
The length of the wooden cylinder is given as 17.5cm, which is already in the correct unit.
4. Calculate the volume of the wood:
The volume of a cylinder is calculated using the formula V = πr^2h. In this case, the radius of the wooden cylinder is 5mm (or 0.5cm) and the length is 17.5cm. So, the volume of the wood is V = π * (0.5cm)^2 * 17.5cm.
5. Calculate the volume of the graphite:
The volume of a cylinder is calculated using the formula V = πr^2h. In this case, the radius of the graphite cylinder is 1.5mm (or 0.15cm) and the length is 17.5cm. So, the volume of the graphite is V = π * (0.15cm)^2 * 17.5cm.
Now, let's calculate the values.
- The volume of the wood:
V = π * (0.5cm)^2 * 17.5cm
V = 3.14 * 0.25cm^2 * 17.5cm
V ≈ 1.96cm^3
- The volume of the graphite:
V = π * (0.15cm)^2 * 17.5cm
V = 3.14 * 0.0225cm^2 * 17.5cm
V ≈ 0.97cm^3
Therefore, the volume of the wood is approximately 1.96 cubic centimeters, and the volume of the graphite used is approximately 0.97 cubic centimeters.