there is a groove which is in a cylindrical form and 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

volume of whole cylinder

= π(5^2)(175) mm^3 = 4375π mm^3

volume of graphite
= π(1.5^2)(175
= 393.75π mm^3

volume of wood = 4375π - 393.75π = 3981.25π mm^3
= appr 12507.5 mm^3

To find the volume of the wood, we need to calculate the volume of the cylinder. The formula for the volume of a cylinder is given by V = πr^2h, where V is the volume, r is the radius, and h is the height (or length in this case) of the cylinder.

First, let's find the radius of the wooden cylinder. The diameter is given as 10mm, so the radius (r_w) can be calculated as half of the diameter. Therefore, r_w = 10mm / 2 = 5mm = 0.5cm.

Next, we can substitute the values of r_w and h into the formula to calculate the volume of the wood:

V_wood = π(0.5cm)^2(17.5cm)
= π(0.25cm^2)(17.5cm)
≈ 3.14 * 0.0625cm^2 * 17.5cm
≈ 0.03490625 * 17.5cm
≈ 0.610859375 cm^3

Therefore, the volume of the wood is approximately 0.610859375 cm^3.

To find the volume of the graphite, we need to calculate the volume of the cylindrical graphite block. Again, we can use the formula for the volume of a cylinder, but this time using the radius and length of the graphite block.

The diameter of the graphite cylinder is given as 3mm, so the radius (r_g) can be calculated as half of the diameter. Therefore, r_g = 3mm / 2 = 1.5mm = 0.15cm.

Now, substitute the values of r_g and h (which is also 17.5cm) into the formula to calculate the volume of the graphite:

V_graphite = π(0.15cm)^2(17.5cm)
≈ 3.14 * 0.0225cm^2 * 17.5cm
≈ 0.07065 * 17.5cm
≈ 1.238125 cm^3

Therefore, the volume of the graphite used is approximately 1.238125 cm^3.