A wooden lead pencil is in the shape of a cylinder. The pencil is 21cm long with a radius of 0,4cm and its lead is of radius0,1cm.what is the volume of wood in the pencil?

To find the volume of wood in the pencil, we first need to find the volume of the entire pencil and then subtract the volume of the lead.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

For the wood part of the pencil:
V_wood = π(0.4)^2(21) = 33.408 cm^3

Now, we need to find the volume of the lead:
V_lead = π(0.1)^2(21) = 0.6615 cm^3

Therefore, the volume of wood in the pencil is:
V_wood - V_lead = 33.408 - 0.6615 = 32.7465 cm^3

So, the volume of wood in the pencil is 32.7465 cm^3.

Step 1: Calculate the volume of the entire pencil cylinder.

Volume of cylinder = πr²h

where r is the radius (0.4 cm) and h is the height (21 cm)

Volume of entire pencil = π(0.4)²(21) = 26.4π cm³

Step 2: Calculate the volume of the lead cylinder.

Volume of cylinder = πr²h

where r is the lead radius (0.1 cm) and h is the same as the pencil height (21 cm)

Volume of lead = π(0.1)²(21) = 2.1π cm³

Step 3: Calculate the volume of the wood by subtracting the lead volume from the entire pencil volume.

Volume of wood = Volume of entire pencil - Volume of lead

Volume of wood = 26.4π - 2.1π = 24.3π cm³

Therefore, the volume of wood in the pencil is approximately 24.3π cm³.